IMPORTANT QUESTIONS IN ENGINEERING DRAWING

CONIC SECTIOS:

1 . Construct two branches of a hyperbola when its transverse axis is 50 mm long and foci are 70 mm apart. Locate its directrix and determine the eccentricity.

2. Construct an ellipse of major diameter 120mm and minor diameter 80mm using concentric circle method. 3. Draw the hyperbola when the focus and the vertex are 25 mm apart. Consider eccentricity as 3/2. Draw a tangent and normal to the curve at a point that is 35 mm from the focus.

44 The major axis of an ellipse is 120 mm long and the foci are at a distance of 20 mm from its ends. Draw the ellipse using one-half of it by concentric circles method and the other half by rectangle method.

55 Draw an ellipse when the distance of its focus from the directrix is 60 mm and eccentricity is 2/3. Draw tangent and normal to the curve at a point 40 mm from focus.

6. Draw a parabola in the parallelogram of sides 120 mm and 80 mm, take the longer side as horizontal base. Consider one of the included angles between the sides as 60 degrees.

7. Draw a parabola when span is 80 mm and rise is 30 mm using tangent method.

8. Draw a parabola when span and rise are 100 mm and 80 mm respectively. Draw the curve using rectangle method

9. Draw a path of a ball which is thrown from ground level which reaches a height of 30 m and a horizontal distance of 60 m before return to the ground. Name the curve.

10. Draw the hyperbola when its vertex and its focus are at a distance of 40 mm and 25 mm respectively from the directrix. Plot at least six points.

11. Construct an ellipse of major diameter 120 mm and minor diameter 80 mm using concentric circle method for half of the curve and oblong method for the other half of the curve.

12. The major axis of an ellipse is 120mm long and the foci are at a distance of 20mm from its ends. Draw the ellipse using one-half of it by concentric circles method and the other half by rectangle method.

13. The focus of a hyperbola is 35 mm from its directrix. Draw the curve when eccentricity is 4/3. Draw a tangent and a normal to the curve at a point 30mm from the focus. Trace a conic section when the distance of the focus from the DirectX is 40mm and eccentricity is equal to equal to 9/7. Name the curve. Draw a tangent and normal to the curve from a point on it, which is at a distance of 30mm from the focus.

CYCELOIDS:

1. A circle having a 50 mm diameter rolls within a circle with a 150 mm diameter with internal contact. Draw the locus of a point lying on the circumference of the rolling circle for its complete turn. Name the curve. Also draw a tangent and a normal to the curve, at a point that is 40 mm from the centre of the bigger circle.

2. Draw the locus of a point lying on the circumference of a circle having a 70 mm diameter, which rolls on a circle with a 140 mm diameter with internal contact for one complete rotation.

3. A fixed point is 90 mm from the fixed straight line. Draw the locus of a point P moving in such a way that its distance from the fixed point is twice its distance from the fixed straight line. Name the curve.

4. A circle of 40mm diameter rolls inside the circumference of another circle of 80mm diameter. Draw the locus of any point on the rolling circle for one complete revolution of the rolling circle. Name the curve.

5. A bicycle wheel of 1mt diameter rolls on a straight surface. The point P is on the spoke of the wheel at a distance of 0.2mt from the rim. Draw the locus of the point P for one complete revolution of the wheel. Name the curve.

6. A circular disc of 50mm diameter rolls outside the circumference of another circle of 140mm diameter for one complete revolution without slipping. Trace the path of a point P which is situated at a distance of (a) 30mm from the center of the rolling circle (b) 20mm from the center of the rolling circle. Name the curve.

7. ABC is an equilateral triangle of side 70mm. Trace the loci of vertices A,B and C. when the circle circumscribing ABC rolls without slipping along a fixed straight line, for one complete revolution.

8. A circus man rides a motor cycle inside a globe of diameter 4mts. The motor cycle wheel is 0.8mts in diameter. Draw the locus of a point on the circumference of the motor cycle wheel for its one complete revolution. Name the curve.

INVOLUTES:

1. Draw the path that would be traced by an end of the string, when it is unwound from the circumference of the disc, which is in the form of a square having a 30 mm side surmounted by semicircles on opposite sides.

2. Draw the involute of a hexagon of 25 mm side for one convolution. Draw tangent and normal to the curve from a point on it.

3. An elastic string of length has its one end attached to the circumference of circle of 50 mm diameter. Draw the curve traced by the other end of the string when it is tightly wound round the circle when L=100 mm. Draw a tangent and normal to the curve.

SCALES:

1. The distance between two stations is 130km. a train covers this distance in 2.5 hours. Construct a plain scale to measure time up to a single minute. The RF of the scale is 1:260000. Find the distance covered by the train in 45 minutes.

2. Draw a plain scale of RF 1:40 to read Meters and Decimeters and long enough to measure up to 8m. Show lengths of 4.3m and 6.2m on this scale.

3. The R.F. of a scale is 1/400. Construct the scale to measure a maximum distance of 50 m and show a distance of 37.6 m on it. Name the scale and find length of the scale.

4. The distance between two stations by road is 200 km and it is represented on a certain map by a 5 cm long line. Find the R. F. and construct a diagonal scale showing a single kilometer and long enough to measure up to 600 km. Show a distance of 467 km on this scale.

5. Construct and name the scale of R.F. 1: 250 to show decimeter and long enough to measure up to 30 m. indicate a distance of 28.9 m on it.

6. Construct a diagonal scale of 1:25 to read meters, decimeters and centimeters and long enough to measure 4m. Mark on it a distance of 2.47m.

7. A room of 1728 m3 volume is shown by a cube of 4 cm side. Find the R.F. and construct a scale to measure up to 50 m. Also indicate a distance of 37.6 m on the scale.

8. An area of 400 cm2 on a map represents an area of 25m2 on a field. Construct a scale to measure up to 5 km and capable to show a distance of 3.56 km. Indicate this distance on the scale.

9. The distance between two points on a map is 15 cm. The real distance between them is 20 km. Draw a diagonal scale to measure up to 25 km and show a distance of 13.6 km on it.

10. Construct and name the scale of R.F. 1:250 to show decimeter and long enough to measure up to 30m. Indicate a distance of 28.9 m on it.

11. The R.F.of a scale is 1/400. Construct the scale to measure a maximum distance of 50 m and show a distance of 37.6m on it. Name the scale and find length of the scale.

12. A cube of 5cm sides represents a tank of 1000 m3 volume. Find the R.F. and construct a scale to measure up to 35m and mark a distance of 27 m on it.

13. A line 1 cm long represents a length of 4 decameter. Draw a plain scale and mark a distance of 6.7 m on it. Find RF and length of the scale.

14. An area of 49 sq cm on a map represents an area of 16 m2 on a field. Draw a scale long enough to measure 8 m. Mark a distance of 6 m 9 dm on the scale. Find RF and length of the scale.

15. Construct a diagonal scale showing kilometer, hectometer and decameter in which a 2 cm long line represents 1 km and the scale is long enough to measure up to 7 km. Find R.F. and mark 4 km 5 hm3 dm on it.

POINTS:

1. Two points A and B are in the H.P. the point A is 30 mm in front of the VP. While B is behind the V.P. The distance between their projections is 75 mm and line joining their top views makes an angle of 450 with xy. Find the distance of the point B from the V.P.

2. A point C is 40mm below H.P and 20mm behind V.P, another points D and E are 60mm above H.P and in front of V.P, 90 mm below H.P and 45mm in front of V.P respectively draw the projections of all points on same reference line.

LINES:

1. A line AB, 75mm long is in second quadrant with the end, A in the HP and the end, B in the VP. The line is inclined at 300 to HP and at 450 to VP. Draw the projections of AB and determine its traces.

2. A line PQ is 75 mm long and lies in an auxiliary inclined plane which makes an angle of 450with the H.P. The front view of the line measures 55 mm and the end P is in V.P and 20 mm above H.P. Draw the projections of PQ and find its inclinations with both the planes and their traces.

3. The projections of the ends of a line AB are on the same projector. The end A is 30 mm below H.P and 15 mm behind V.P. The end B is 35 mm above H.P and 40 mm in front of V.P. Determine its true length, traces and the inclinations with the reference planes.

4. A line AB measures 100 mm. The projectors through its V.T and the end A are 40 mm apart. The point A is 30 mm below H.P and 20 mm behind V.P. The V.T is 10 mm above H.P. Draw the projections of the line and determine its H.T and inclinations with H.P and V.P.

5. A line EF 85 long has its ends 25 mm above HP and 20 mm in front of V.P. The top and front views of the line have lengths of 55 mm and 70 mm respectively. Draw the projections of the line and find its true inclinations with the V.P and H.P.

6. The front view of a line AB 80 mm long measures 55 mm while its top view measures 70 mm. End A is in both HP and VP. Draw the projections of the line and find its inclinations with the reference planes. Also locate the traces.

7. The front view of a line AB measures 65mm and makes an angle of 45 with xy. A is in the H.P and the V.T of a line is15 mm below the H.P. The line is inclined at 30 to the V.P. Draw the projections of AB and find its true length and inclination with the H.P. Also locate its H.T.

8. The top view of a 75 mm long line AB measures 65 mm, while the length of its front view is 50 mm. Its one end A is in the H.P and 12 mm in front of the VP. Draw the projections of AB and determine its inclinations with the H.P and the V.P.

9. A 80 mm long line AB is inclined at 450 to the H.P and 300 to the V.P. Its end A is in the H.P. and 40 mm in front of the V.P. Draw its projections keeping the end B in the fourth quadrant.

1. The end point C of an 80 mm long line CD is 15 mm above the H.P. and 10 mm in front of the V.P. The line is inclined at 300 to the H.P. and 450 to the V.P., and the other end point D lies in the second quadrant. Draw its projections and determine its traces.

2. The HT and the VT of a straight line AB is below and above XY respectively. The distance between the HT and the VT as measured parallel to XY is 200mm. The end B of the line is nearer to the VP than the end A. The view from above of the line makes 300 to XY. The end B is 10 mm from the VP and 20 mm from the HP. The distance between the end projectors of the line measures 50mm parallel to XY. Draw the projections of the line.

3. The end A of a straight line AB is 10 mm from the VP and 20 mm from the HP. The end B is 30 mm from the VP and 40 mm from the HP. The VT of the line is 20 mm from the end A as measured parallel to XY. Draw the projections and find the TL and the inclinations of the line.

4. A line PQ, 64 mm long has one of its extremities 20 mm in front VP and the other 50 mm above HP. The line is inclined at 400 to HP and 250 to VP. Draw its top and front views.

5. The projections of a line AB ha 350 inclination in top view and 400 inclination in the front view with an elevation length of 60 mm. If the end A is 10 mm below HP and B is 12 mm behind VP, draw the projections and locate the traces keeping the line in the third quadrant.

6. Line PQ has 72 mm length in the front view and 66 mm length in the top view. The end P is 48 mm below HP and 40 mm behind VP, while the end Q is 12 mm below HP. Draw the projection of the line, locate the traces and determine the true length and inclinations of the line with the reference planes.

7. Line CD is in the second quadrant and has 250 inclination with HP, while the front view has 300 inclination with xy line and 60 mm length. If the end C is 12 mm above HP and the end D is 60 mm behind VP, draw its projections.

8. The projectors of the ends of a line AB are 55 mm apart. The end ‘A’ is 35 mm above HP and 40 mm in front of V.P. The end ‘B’ is 15 mm below the H.P and 45 mm behind V.P. Determine true length and its inclinations with two planes.

9. The top view of a 75 mm long line measures 60 mm, while its front view is 55 mm. Its one end A is 10 mm above H.P and 15 mm in front of V.P. Draw the projections of the line and determine its inclinations with H.P & V.P.

10. A line AB of 75 mm long has its end ‘A’ 20 mm above H.P and 15 mm in front of V.P. The line is inclined at 300 to H.P. and 500 to V.P. Draw the projections find the traces.

11. The mid-point of a straight line AB is 60 mm above H.P and 50 mm in front of V.P. The line measures 80 mm and inclined at 300 to H.P & 450 to V.P. Draw the projections.

12. A line CD 60mm long has its end ‘C’ in both H.P and V.P. It is inclined at 300 to H.P and 450 to V.P. Draw the projections. The end P of a straight line PQ is 20 mm above the H.P. and 30 mm in front of V.P. The end Q is 15 mm below the H.P. and 45mm behind the V.P. If the end projectors are 50 mm apart, Draw the projection of PQ and determine the true length, traces and inclination with the reference planes.

13. The front view of line inclined at 300 to V.P is 65mm long. Draw the projections of a line, when it is parallel to and 40mm above H.P. and one end being 20mm in front of V.P.

PLANES:

1. A thin rectangular plate of sides, 60 mm × 30 mm has its shorter edge in V.P and that shorter edge is inclined at 300 to H.P. Project its top view if its front view is a square of 30 mm long.

2. A hexagonal plate of side, 40mm, is resting on a corner in VP with its surface making an angle of 300 with the VP. The front view of the diagonal passing through that corner is inclined at 450 to the line, xy. Draw the projections of the plate using auxiliary plane method.

3. A thin pentagonal plate of 60 mm long edges has one of its edges in the H.P and perpendicular to V.P while its farthest corner is 60 mm above the H.P. Draw the projections of the plate. Project another front view on Auxiliary Vertical Plane (A.V.P) making an angle of 450 with V.P.

4. A regular hexagonal lamina with its edge 50 mm has its plane inclined at 450 to H.P and lying with one of its edges in H.P. The plane of one of its diagonals is inclined at 450 to XY. The corner nearest to VP is 15mm in front of it. Draw its projections.

5. A regular pentagon lamina of 30 mm side surface is inclined at 300 to V.P and side on which it rests of VP makes at angle of 450 to HP. Draw its projection by auxiliary plane method.

6. An isosceles triangular plane ABC with a 70 mm base and altitude 80 mm has its base in the H.P. and inclined at 450 to the V.P. The corners A and C are in the V.P. Draw its projections and determine the inclination of the plane with H.P.

7. A square lamina is placed such that one of the corners is touching the VP and the diagonal through this is perpendicular to the VP and measures 60mm. The other diagonal appear to be 40 mm in the view from above. Draw the projections and find the inclination of the plane to the ground.

8. A pentagonal plane with a 35 mm side is resting on one of its edges in the H.P. with its surface perpendicular to the V.P. The corner opposite to the edge on which it is resting is 40 mm above the H.P. draw its projections. Also, project another front view on an A.V.P. which is inclined at 450 with the V.P.

9. A pentagon of side 30 mm is resting on an edge in H.P, such that it makes an angle of 500with V.P and its surface makes an angle of 300 with H.P. Draw the projections.

10. A Rhombus of diagonals 120 mm & 80 mm is resting on one of its corners in H.P such that the longer diagonal is inclined at 300 to H.P and the shorter diagonal is parallel to both the planes.

11. A hexagon of 30 mm side is resting on one edge in V.P and making an angle of 300 to H.P. Its surface makes an angle of 450 to V.P. Draw the projections.

12. Draw the projections of a circle of 50 mm diameter having a point on the circumference of the circle in H.P, such that its surface makes an angle of 400 with H.P. and the top view of the diameter passing through that point makes an angle of 300 with V.P. Draw the projections.

13. A regular pentagon of 30mm side has one side on the ground and its plane is inclined at 450 to H.P and perpendicular to V.P. Draw the projections

1. A plate having shape of an isosceles triangle has base 50 mm long and altitude 70 mm. It is so placed that in the front view it is seen as an equilateral triangle of 50 mm sides one side inclined at 450 to xy. Draw its top view.

2. A thin circular plate of 40mm diameter having its plane vertical and inclined at 400 to V.P. Its center is 30mm above H.P. and 35mm in front of V.P. draw the projections.

SOLIDS:

1. A pentagonal pyramid has an edge of the base in the V.P is inclined at 300 to the H.P., while the triangular face containing that edge makes an angle of 450 to the V.P. Draw the three views of the pyramid, if the edge of the base is 30 mm and that of axis is 80 mm.

2. A hexagonal pyramid base 25 mm side and axis 55 mm long has one of its slant edges on the ground. A plane containing that edge and the axis is perpendicular to the H.P and inclined at 450 to the V.P. Draw its projections when the apex is nearer the V.P than the base.

3. A pentagonal pyramid, base 25mm side and axis 50mm long has one of its triangular faces in the V.P. and the edge of the base contained by that face makes an angle of 30 with the H.P. Draw its projections.

4. A tetrahedron of edge 50 mm long is standing on one of its corners on the ground with one of the edges connected with this corner making 600 with the ground and one of the triangular faces connected with this corner making an angle of 300 with the VP. Draw the projection of the object.

5. A triangular prism of base side 40 mm and height 50 mm has its axis inclined at 400 to VP and has a base edge on VP, inclined at 500 to HP. Draw its projections.

6. A rectangular prism of base 40 mm x 30 mm and height 70 mm rests with is longer edge of the base on the VP. If the axis of the prism is inclined to VP at 300 and the front view of the axis is inclined to the xy line at 450, draw the top and

front views.

7. A square pyramid with side of base 40 mm and height 80 mm is suspended freely from a point on a slant edge at distance of 20 mm from its apex. The top view of the axis of the pyramid is inclined at 300 to the xy line. Draw the projections.

8. A right circular cone of base diameter 60 mm and height 80 mm is so placed that diameter KJ of the base is inclined at 500 with HP and the other diameter LM of the base is parallel to both HP and VP. Draw the top and front views of the cone. The diameters KJ and LM are perpendicular to each other.

9. A square pyramid of 30 mm side and 60 mm height is resting on one of its triangular faces in H.P, such that the edge containing that face makes an angle of 300 with V.P. Draw the projections of the pyramid.

10. A Hexagonal pyramid of the base 30 mm and axis 65 mm long is resting on an edge of the base in H.P, and makes an angle of 450 with V.P, and axis of the pyramid makes an angle of 300 with H.P. Draw the projections of pyramid.

1. A tetrahedron of 60 mm long edges is resting on one of edges in H.P and inclined at 400 to V.P, while the face containing that edge is vertical. Draw the projections.

2. Draw the projections of a pentagonal prism, base 25 mm side and axis 50 mm long resting on one of its rectangular faces on H.P., with the axis inclined at 45 degrees to V.P.

3. A pentagonal prism having base with a 30 mm side and a 75 mm long axis, has one of its rectangular faces on H.P. and the axis is inclined at 60 degrees to the V.P. Draw its projections.

4. Draw the projections of a hexagonal pyramid of side of base 30mm and axis 60mm long resting on one of its base edges in H.P with its axis inclined at 300 to H.P. and the top view of axis is 450 to V.P.

SECTIONS AND DEVELOPMENTS

1. A pentagonal pyramid base 30 mm side and axis 60 mm long lying on one of its triangular faces on the HP with the axis parallel to VP. A vertical section plane whose H.T bisects the top view of the axis and makes an angle of 30 degrees with reference line cuts the pyramid removing its top part. Draw the top view, sectional front view and true shape of the section.

A vertical hexagonal prism of 25 mm side of base and axis 60 mm has one of its rectangular faces parallel to VP. A circular hole of 40 mm diameter is drilled through the prism such that the axis of the hole bisects the axis of the prism at right angle and is perpendicular to VP. Draw the development of the lateral surface of the prism showing the true shape of the hole in it.(development)

A square pyramid, base 50mm side and axis 75mm long, is resting on the H.P. on one of its triangular faces, the top view of the axis making an angle30 with the V.P. It is cut by a horizontal section plane, the V.T. of which intersects the axis at a point 6mm from the base. Draw the front view, sectional top view and the development of the sectioned pyramid.

A hexagonal prism side of base 35 mm and height 75 mm is resting on one of its corners on the H.P with a longer edge containing that corner inclined at 600 to the H.P and a rectangular face parallel to the V.P. A horizontal section plane cuts the prism in two equal halves. i) Draw the front view and sectional top view of the cut prism ii) Draw another top view on the auxiliary inclined plane which makes an angle of 450 with the H.P.

5. A cylinder, 65 mm diameter and 90 mm long has its axis parallel to the H.P and is inclined at 300 to V.P. It is cut by a vertical section plane in such a way that the true shape of the section is an ellipse having a major axis, 75 mm long. Draw its sectional front view and true shape of the section.

6. Draw the development of the lateral surface of the truncated triangular pyramid resting on H.P with one of its edges perpendicular to V.P and is cut by a plane inclined at 300 to H.P and the plane is passing through the axis at a distance of 20 mm from the vertex. The edge of the base is 30 mm and the length of the axis is 40 mm

7. A square pyramid, base 50 mm side and axis 75 mm long, is resting on H.P on one of its triangular faces, the top view of the axis making an angle of 300 with V.P. It is cut by a horizontal section plane, the V.T of which intersects the axis at a point 6 mm from the base. Draw the front view, sectional top view and the development of the sectioned pyramid

A cone, base 65 mm diameter and axis 75 mm long, is lying on H.P on one of its generators with the axis parallel to V.P. A section plane which is parallel to V.P cuts the cone 6 mm away from the axis. Draw the sectional front view and the development of the surface of the remaining portion of the cone.

1. A pentagonal prism of base edge 30 mm and height 70 mm is placed with one of its rectangular faces on the ground and the axis parallel to the VP. It is cut by a section plane perpendicular to the VP and inclined at 300 to the ground. It passes through the midpoint of the axis. Develop the remaining surface of the object.

2. Draw the development of the lateral surface of the truncated right circular cylinder of diameter 44 mm and height 70 mm. The tube is placed on HP. A section plane, passing through the geometrical centre of the top face of the tube, perpendicular to VP and inclined at 450 to HP, cuts off the top portion of the tube. A similar section plane making an angle of 300 to HP in the opposite direction cuts the axis at a height of 14 mm from the base

3. A cylinder, with a 60 mm base diameter and a 70 mm long axis, is lying on a generator on the H.P with its axis parallel to the V.P. A vertical section plane, the H.T. of which makes an angle of 300 with the V.P. and passes through a point distant 25 mm on the axis from one of its ends, cuts the cylinder. Draw its sectional front view and obtain the true shape of the section.

4. A hexagonal prism, having a base with a 20mm side and 60mm height is resting on the base in HP such that one of the rectangular faces is parallel to the VP. It is cut by a plane perpendicular to VP and 60 degrees inclined to HP and cutting the midpoint of the axis of the solid. Draw development of lateral surface of the bottom part of the solid.

5. A square prism, having a base with a 30mm side and 60mm height is resting on the base in HP such that one of the rectangular faces is parallel to the VP. It is cut by a plane perpendicular to VP and 60 degrees inclined to HP and bisecting the axis of the solid. Draw development of lateral surface of the bottom part of the solid.

6. A pentagonal prism, having a base with a 30mm side and 60mm height is resting on the base in HP such that one of the rectangular faces is parallel to the VP. It is cut by a plane perpendicular to VP and 45 degrees inclined to HP and cutting the axis of the solid 10mm from the top. Draw development of lateral surface of the bottom part of the solid.

7. A hexagonal pyramid, having a base with a 20mm side and 50mm height is resting on the base in HP such that one of the base sides is parallel to the VP. It is cut by a plane perpendicular to VP and 60 degrees inclined to HP and bisecting the axis of the solid. Draw development of lateral surface of the bottom part of the solid.

8. A square pyramid, having a base with a 30mm side and 60mm height is resting on the base in HP such that one of the base sides is parallel to the VP. It is cut by a plane perpendicular to VP and 45 degrees inclined to HP and cutting the axis of the solid 20mm from top. Draw development of lateral surface of the bottom part of the solid.

A square pyramid, having a base with a 40 mm side and a 60 mm long axis, is resting on its base on the ground with all the edges of the base equally inclined to the V.P. It is cut by an A.I.P. such that true shape of the section is an equilateral triangle of largest side. Draw the sectional top view and true shape of the section.

2. A cone with base circle diameter 50mm and 60mm height is resting on the base in HP. It is cut by a plane perpendicular to VP and 60 degrees inclined to HP and bisecting the axis of the solid. Draw development of lateral surface of the bottom part of the solid.

INTERSECTIONS OF SOLID

1. A cone of base diameter 70 mm and altitude 80 mm is resting on HP on its base. It is penetrated by a cylinder of diameter 30 mm and the axis is parallel to both HP and VP. The axis of the cylinder is situated at a distance 20 mm above the base of the cone and 5 mm away from the axis of the cone and is towards the observer. Draw the curves of intersection of the solids.

2. A cylinder of diameter 30 mm penetrates into a cylinder of diameter 60 mm. Their axes intersect each other at an angle of 60°. Draw the front view and top view of the solids showing the curves of intersection.

3. A vertical cylinder 70mm diameter is penetrated by another cylinder of the same size and its axis is parallel to both HP and VP. Axis of vertical cylinder is 10mm away from the axis of horizontal cylinder. Draw the projections showing curves of intersection.

4. A cone, diameter of base 90 mm and altitude 80mm rests with its base on ground. A vertical cylinder of 40 mm diameter has its axis 5 mm in front of that of the cone and the axes are contained in a plane making an angle of 30 degrees with the VP. Draw the curves of penetration of the surface.

5. A vertical cone 80 mm diameter of base and axis 100 mm long is penetrated by a vertical cylinder of 60 mm diameter and 100 mm long such that the top circular end of the cylinder contains the apex of the cone and a plane perpendicular to both HP and VP containing the axes of both the solids and the axis of the cylinder is at a distance of 10 mm from the axis of the cone and is towards the observer. Draw the top and front view of the solids showing the curves of intersection.

6. A vertical square prism with 50 mm sides and 100 mm length has its side faces equally inclined to the VP. It is completely penetrated by a horizontal cylinder 60 mm in diameter and 100 mm in length. The axes of the two solids bisect each other perpendicularly. Draw the projections showing curves of intersection when the plane containing the two axes is parallel to the VP.

7. A cylinder of 60 mm diameter having its axis vertical is penetrated by another cylinder of 40 mm diameter. The axis of the penetrating cylinder is parallel to VP and bisects the axis of the vertical cylinder marking an angle of 60° with it. Draw the orthographic projections showing the curves of intersection.

8. A cylinder of diameter 50 mm penetrates fully into a cone of base diameter 80 mm altitude 110 mm, which is resting on its base on HP. The axis of the cylinder intersects the axis of the cone at right angles at a height of 30 mm above the base of the cone. The axis of cylinder is parallel to both the planes. Draw the projections of the solids showing the curves of intersection.

9. A cylinder of diameter 44 mm pierces through a vertical cylinder of diameter 44 mm. The axis of the piercing cylinder is parallel to both the HP and VP. The axes are separated by distance of 6 mm, the axis of the horizontal cylinder being nearer to the observer. Draw the curves of intersection.

A A vertical cylinder 80mm diameter is penetrated by another cylinder of the same size and its axis is parallel to both HP and VP. Axis of vertical cylinder is intersecting the axis of horizontal cylinder. Draw the projections showing curves of intersection.

1. A horizontal cylinder 40 mm diameter and axis length 75 mm centrally penetrates vertical cylinder 50 mm as base diameter. Draw the plan and elevation, showing curves of intersection. Assume the axis of the horizontal cylinder is parallel to VP.

2. A horizontal cylinder of 50 mm diameter penetrates a vertical cylinder of 75 mm diameters resting on HP. The two axes are coplanar. The axis of the horizontal cylinder is 50 mm above the HP. Draw the projection showing the curves of intersection.

3. A vertical cylinder of 60 mm diameter and 80 mm height is penetrated by a horizontal cylinder 40 mm diameter and 80 mm long. The axis of the penetrating cylinder is parallel to VP and 6 mm in front of the axis of the vertical cylinder. Draw the projections and show the intersection curve.

ISOMETRICS PROJECTIONS

1. A hexagonal prism of base edge 30 mm and height 70mm long is resting on its rectangular face on the ground with its axis parallel to the VP. A square prism of 20 mm base edge and height 40 mm rests on its base on the top rectangular face of the hexagonal prism. The axis of the square prism intersects and bisects the axis of the hexagonal prism when produced. One of the base edges of the square prism is parallel to the VP. Draw an isometric projection of the set up.

2. A pentagonal prism of base edge 30mm and 50mm long rests on its longer edge on the ground with the face opposite to this edge parallel to the ground. A cube of 25mm edge rests on this face on one of its faces. Two adjacent base edges of the cube make equal inclinations to one of the longer edges of the face parallel to the ground. A sphere 30mm diameter rests centrally on the top of the cube. Draw the isometric projections of the arrangement of the solids

3. A sphere with a 50 mm diameter rests centrally over a cube with a 60 mm side. Draw its isometric projection

4. Draw the isometric view of the object whose orthographic projections are shown in figure.

5. Draw the isometric view of a Door-Steps having three steps of 22cm tread and 15cm rise. The steps measure 75cm widthwise.

6. A solid is in the form of a cylinder of base diameter 50 mm up to a height of 60 mm and thereafter tapers into a frustum of a cone of top diameter 30 mm. The total height of the solid is 90 mm. Draw the isometric projection of the solid.

7. A masonry pillar is in the form of a frustum of a hexagonal pyramid. The pillar is of 2 m height and side of its base and top base are 0.5 m and 0.3 m respectively. Draw its isometric projection.

8. Draw isometric view of a cylinder of base diameter 55 mm and axis length 65 mm when the axis of the cylinder is (i) vertical (ii) horizontal.

9. Draw an isometric view of a hexagonal prism having a base with 25 mm side and a 65 mm long axis, which is lying on its face in the H.P. with axis parallel to both H.P. and V.P.

10. A vertical cylinder of base diameter 50 mm and height 70 mm is cut by a plane inclined at 550 to HP and perpendicular to VP, which meets the axis at a distance of 20 mm from top base. Draw the isometric view of the remaining portion of the cylinder.

11. A square pyramid having a side of 50 mm base and 75 mm as axis height stands centrally on circular block of 100 mm diameter and 50 mm thick. The base edges of the pyramid are parallel to VP. Draw the isometric projection of the two objects.

12 A pentagonal pyramid of base of side 30 mm rests on the top of a pentagonal prism of side 30 mm, with their sides coinciding with each other. The solid stands on HP with one of the sides of the base perpendicular to the VP. The height of prism = 40 mm. The height of pyramid = 50 mm. Draw the isometric projection of the solid.

13 A frustum of a cone 30 mm as top diameter, 50 mm as bottom diameter and 60 mm long is placed vertically on a square slab of side 70 mm and 30 mm thick, such that both the solids have the common axis. Draw the isometric projection of the combination of solids.

14 Draw an isometric projection of a frustum of the pentagonal pyramid with a 40 mm base side, 20 mm top side and 35 mm height resting on its base in the H.P.

15 A hexagonal prism with a 30 mm base and 45 mm axis has an axial hole with a 30 mm diameter. Draw its isometric projection. When its axis is perpendicular to H.P. and two Rectangular faces are parallel to V.P.

16 A square prism, side of base 4 cm and 8 cm long rests centrally on a cylindrical slab 6cm diameter and 3 cm thick. Draw the isometric projection of the solid.

17 A cone of base diameter 30 mm and height 40 mm rests centrally over a cube of sides 50mm. draw the isometric projection of the combination of solids.

18 A sphere of diameter 45 mm rests centrally over a frustum of cone of base diameter 60 mm. top diameter 40 mm and height 60 mm. draw isometric projections of the Combination of solids.

19 A hexagonal pyramid of base side 30 mm and axis length 70 mm is resting on HP on its base with a side of base parallel to VP. It is cut by a plane inclined at 40° to HP and perpendicular to VP and bisects the axis. Draw the isometric view of the lower part of the pyramid.

20 A triangular pyramid having base with a 60 mm side and an 80 mm long axis is resting on its base in the H.P. with a side of base perpendicular to the V.P. It is cut by an A.I.P. making an angle of 450 with the H.P. and bisecting the axis. Draw its isometric view of the bottom portion.(UPDATED)

21 A sphere with a 50 mm diameter rests centrally over a cube with a 60 mm side. Draw its isometric projection.

22 The frustum of a sphere with a 80 mm diameter and frustum circle with a 50 mm diameter is used as a paper weight. Draw its isometric projection.

23 A sphere of 60mm diameter is intersected by a cylinder of 30mm diameter. The axis of the cylinder passes through the centre of the sphere. The tip of the axis of the cylinder is 70mm from the centre of the sphere. Draw the isometric projection of the objects when the axis of the cylinder is parallel to both the VP and the HP.

24 A hexagonal prism having base with a 30 mm side and a 70 mm long axis is resting on its base on the H.P. with a side of base parallel to the V.P. It is cut by an A.I.P. making 450with the H.P. and bisecting the axis. Draw its isometric projection.

13. Draw the isometric view of a cylinder of 60 mm height and diameter 44 mm, lying on one of its generators on HP with the axis perpendicular to VP. Select the origin of the isometric axes suitable to get the front view on the right isometric plane.

25. A cylinder of diameter 50 mm base and 70 mm height is resting upon its base on HP. A section plane of 600 inclination to Hp cuts the axis of the cylinder at a height of 55 mm from the base. Draw the isometric view of the cylinder showing the sectioned surface.

26 A pentagonal pyramid of height 60 mm and side 28 mm is resting on HP, keeping its axis vertical and one edge of the base parallel to VP. Draw isometric view of the solid.

PERSPECTIVE PROJECTIONS

1. A rectangular prism of 110X70X40 mm size is lying on its 110X70mm rectangular face on the ground plane with a vertical edge touching the PP and the end faces inclined at 500 with PP. the station point is 80mm in front of the PP, 65mm above the ground plane and 40mm to the right of the vertical edge that touches the PP. draw the perspective view of the prism.

2. A hexagonal prism side of base 30mm and 65mm long rests with its base on the ground. The nearest vertical edge is 10mm to the left of the eye and 15mm behind the PP. one of the faces containing the edge recedes 450 to the PP, towards the left. The eye is 150mm from the picture plane and is at a height of 801mm. draw the perspective view of the prism.

3. A square pyramid 45mm base edge and 50mm axis rests on its base on the ground such that two parallel base edges recede at 300 to the right of the PP with the nearest corner of the base 10mm behind the PP. the station point is 40mm in front of the PP, 70mm above the GP and 10mm to the right of the nearest corner. Draw the perspective view of the solid.

4. Draw the perspective view of a frustum of a square pyramid with 40mm edges at the base, 30mm at the top, and 50mm in height. The frustum is resting on its base with base edges equally inclined to the PP and one of the base corners touching it. The station point is 80mm in front of the PP, 15mm to the left of the axis of the frustum, and 60mm above the ground plane.

5. Draw the perspective view of a square prism of base 10 cm side and 12 cm height. The nearest edge of the base is parallel to and 3 cm behind the picture plane. The station point is situated at a distance of 30 cm from the picture plane and 6 cm above the ground plane and 20 cm to the right of the apex.

6. Draw the perspective view of a pentagonal prism, lying on the ground plane on one of its rectangular faces, the axis being inclined at 300 to the picture plane, and a corner of the base touching the picture plane. The station point is 6.5 mm in front of the picture plane and lies in the central plane which bisects the axis. The horizon is at the level of the top edge of the prism.

7. A model of steps has three steps of 10 mm tread and 10 mm rise. The length of the steps is 60mm. The model is placed with the vertical edge of the first step touching the PP and its longer edge inclined at 30o to PP. The station point is 70 mm in front of PP, 55mm above the ground plane and lies in a central plane which is at 30 mm to the right of the vertical edge touching the PP. Draw the perspective view.

8. A cube of edge 30 rests with one of its faces on the ground plane such that a vertical edge touches the PP. The vertical faces of the cube are equally inclined to PP and behind it. A station point is 40 mm in front of the PP, 50 mm above the ground plane and lies in a central plane 15 mm to the right of the axis of the cube. Draw the perspective view.

9. Draw the perspective view of a pentagonal prism lying on the ground plane on one of its rectangle faces, the axis being inclined at 38 the picture plane and a corner of the base touching the picture plane the station point is 6.5 cm in front of the picture planes and lies in a central plane which bisects the axis. The horizon is at the level of the top edge of the prism.

10. A rectangular prism of base edges 60mm × 40mm and height 80mm is resting on its broader rectangular face on the ground with the base parallel to the PP. The PP bisects the axis of the object. The station point is on the central line of the object 80mm in front of the PP and 70mm above the ground. Draw the perspective projection of the object.

1). A cylinder of base diameter 50mm and height 80mm is resting on the ground on its base. The object is placed in front of the PP with one of its generators touching the PP. When the base is enclosed in a square, one of the edges of this square makes 40° with the PP. The station point is directly in front of the generator which is touching the PP and 70mm in front of it. The horizon plane is 40mm above the ground. Draw the perspective projection of the object.

2). A square plane with a 60 mm side lies on the GP with the edge nearer to the observer lying in the PP. The station point is 50 mm in front of PP, 60 mm above GP, and lies in a CP which is 50 mm towards right of the centre of the object. Draw its perspective view.

3). A triangular pyramid of base edges 40mm long and axis 70mm is resting on one of the base edges on the ground with the base being parallel to the PP. The apex is nearer to the PP and 20mm behind it. The station point is 50mm to the right of the axis and 60mm from the PP. The horizon is 70mm from the ground. Draw the perspective view of the object.

4). A pentagonal prism, side of base 25 mm and axis 60 mm long, lies with one of its rectangular faces on the ground plane such that a pentagonal face is touching the picture plane. The station point is 20 mm in front of the picture plane, 55 mm above the ground plane and lies in a central plane which is at 80 mm to the right of the centre of the prism. Draw the prospective view.

5). Draw the perspective view of a square pyramid of base 10 cm side and height of the apex 12 cm. The nearest edge of the base is parallel to 3 cm behind the picture plane. The station point is situated at a distance of 30 cm from the picture plane, 6 mm above the ground plane and 20 cm to the right of the apex.

6). A hexagonal plane of 25 mm stands vertically on the ground plane and inclined at 400 to the picture plane. The corner, nearest to picture plane is 25 mm behind it. The station point is 35 mm in front of the picture plane, 45 mm above the ground plane and lies in central plane which passes through the centre of the plane. Draw the perspective view of the plane.

7). A model of steps has three steps of 10 mm tread and 10 mm rise. The length of the steps is 60 mm. The model is placed with the vertical edge of the first step touching the PP and its longer edge inclined at 300 to PP. The station point is 70 mm in front of PP, 55 mm above the ground plane and lies in a central plane

which is at 30 mm to the right of the vertical edge touching the PP. Draw the perspective view.

8). Draw the perspective projection of a hallow cylinder of 60 mm external diameter and 80 mm long, with a wall thickness of 10 mm. It is resting on a generator on the ground, with its axis inclined at 60o to and touching the PP.