Exercise [Development of Surfaces]

EXERCISE

DEVELOPMENT OF PRISM

1. Draw the development of the lateral surface of a right regular hexagonal prism of 24 mm base edge and 56 mm height. An ant moves on its surface from a corner on the base to diametrically opposite corner on the top face by the shortest route. Sketch the path of the ant in the elevation.

2. A cube of side 30 mm rests on its base on HP with a vertical face inclined at 30° to VP. It is cut by a cutting plane perpendicular to VP and inclined at 50° to HP. Cutting plane bisects the axis of the cube. Develop the complete surfaces of the right portion of the cut cube. 

3. A rectangular prism of cross section 45 x 30 mm and height 55 mm rests on the ground on one of its ends with one of its longer edges of the base inclined at 30° to the VP. It is cut by a plane perpendicular to the VP and inclined at 30° to the HP. The plane meets the axis at a point 45 mm above the base. Draw the development of the surfaces of the lower part of the prism. 

4. A hexagonal prism of side of base 25 mm and axis 60 mm long rests on its base on HP with a rectangular face parallel to VP. A square hole of side 35 mm is centrally cut right through the prism such that its axis is perpendicular to VP. Develop the lateral surfaces of the prism with the square slot.

5. A pentagonal prism of side of base 25 mm and axis 60 mm is on HP on one of its ends with a base edge parallel to VP and nearer to it. A square hole of side 25 mm is drilled such that the axis of the hole is perpendicular to VP and bisects the axis of the prism with all the faces equally inclined to HP. Draw the development of the lateral surfaces of the prism showing the true shape of the hole on it.

6. A rectangular prism of sides of base 50 mm x 40 mm and height 80 mm rests on its base on HP such that its vertical faces are equally inclined to VP. It has a horizontal hole of 40 mm diameter drilled through the geometrical center of the prism. The axis of the hole is perpendicular to the axis of the prism. Develop the lateral surfaces of the prism having the hole on it. 

7. A square prism of side of base 45 mm and axis 80 mm long stands on its base on HP with a vertical face inclined at 45° to VP. A circular cut out of 40 mm diameter is drilled through the prism. The center of the cut out is 40 mm above the base and is 15 mm off-set from the axis of the prism. Draw the development of the lateral surfaces of the solid.

DEVELOPMENT OF CYLINDER 

8. A cylinder with a 50 mm base diameter and a 70 mm long axis is resting on its base in HP. It is cut by an auxiliary inclined plane whose V.T is inclined at 30° with the HP and passes through top end of one of the extreme generators. Draw development of the lateral surface of the retained solid.

9. Draw the development of the lateral surface of a cylinder with a 50 mm base diameter and a 70 mm long axis containing a square hole with a 28 mm side. The faces of the square hole are equally inclined to the base of the cylinder and the axis of the hole bisects the axis of the cylinder at right angle.

10. A cylinder with a 60 mm base diameter and 80 mm long axis is resting on its base on HP. A WSTC circular hole with a 44 mm diameter is drilled through the cylinder such that the axis of the hole is perpendicular bisector of the axis of the cylinder. Draw the development of its lateral surface. 

11. A cylinder of 50 mm base diameter and axis 70 mm long rests on its base on HP. A square cut out of 35 mm side is drilled right through the cylinder such that the axis of the cut out is perpendicular to the axis of the cylinder. The center of the cut out is at a distance of 35 mm above HP and 15 mm away from the axis of the cylinder. Two of the faces of the cut out are equally inclined to HP. Develop the lateral surface of the cylinder with the cut out.

12. Draw the development of the lateral surface of each of the cylinders shown below. All the cylinders are of diameter 50 mm and height 70 mm.

DEVELOPMENT OF CONE

13. Draw a frustum of a cone having base diameter 60 mm, top diameter 30 mm and height 25 mm and develop the complete surface of the solid.

14. A cone of base 50 mm diameter and 60 mm height rests with its base on HP. It is cut by a anse section plane perpendicular to VP, parallel to one of the generators and passing through a point on the axis at a distance of 22 mm from the apex. Draw the sectional top view and develop the lateral surface of the remaining portion of the cone. 

15. A cone of 50mm diameter of base and 60mm height is lying on HP on one of its generators with en its axis parallel to VP. It is sectioned by a plane perpendicular to VP, parallel to and 30mm above HP. Draw the development of the lateral surface of the cut cone.

16. A cone of base diameter 70mm and axis 75mm when resting on its base on HP, is cut by a plane parallel to and 50mm above the base. Two more cutting planes normal to VP and 30° to HP cut the cone passing through the base centre on either side. Draw the development of Inom the surface of the mid portion of the cut cone.

17. A right regular cone of 50 mm base diameter and axis 60 mm long stands on its base on HP. A circular hole of 12 mm radius is drilled through the axis of the cone at a height of 15 mm above the base of the cone. Also a square hole of 10 mm side is cut through the axis of the cone at a point 22 mm below the vertex. The sides of the hole are equally inclined to HP. The axes of the holes ae perpendicular to VP. Draw the development of the lateral surface of the cone with the holes in it.

18. A right circular cone of base 60 mm diameter and 60 mm height stands vertically with its base on HP. A semi-circular hole of 36 mm diameter is cut through the cone such that the axis of the hole is parallel to HP, perpendicular to VP and intersecting the axis of the cone 20 mm elor above the base. The flat surface of the hole is parallel to HP and perpendicular to VP. Draw 90s the development of the lateral surface of the cone with the hole.

19. Draw the development of the lateral surface of each of the cones shown below. (Fig. 16.78 to Fig. 16.81). All the cones are of base diameter 60 mm and height 80 mm.

DEVELOPMENT OF PYRAMID

20. A right regular hexagonal pyramid, side of base 30 mm and height 70 mm rests on its base on HP, with one of its base edges 20° inclined to VP. A section plane perpendicular to VP and inclined at 30° to HP, cuts the pyramid, bisecting its axis. Draw the development of the truncated pyramid.

21. A vertical pentagonal pyramid of side of base 27 mm and altitude 50 mm of side rests with a base edge parallel to VP and nearer to it. It is cut by two planes perpendicular to VP. One is horizontal and cuts the portion of the pyramid on the left of the axis at a height of 18mm above y the base of the of teh pyramid. The other plane inclined at 45° to HP cuts the portion of the pyramid to the right of the axis passing through a point on it 18 mm above the base and leans qolevupwards. Draw the development of the lateral surfaces of the truncated pyramid.

22. A Hexagonal pyramid of side of base 25 mm and altitude 70 mm rests on its base on HP such w that a base edge is parallel to VP. It is cut by two cutting planes, perpendicular to VP. One of the planes is inclined at 30° to HP and meeting the axis at a point 40 mm from the base. The other plane is curved of 25 mm radius with the right corner of the base as center. Develop the lateral surfaces of the remaining portion of the pyramid.

23. A pentagonal pyramid (25 x 60) rests on HP on its base with an edge of the base nearer to VP to in and is parallel to VP. It is cut by two planes, both inclined at 45° to HP passing through points on the axis at distances of 20 mm and 25 mm from the apex respectively. Draw the development SH of the cut pyramid. 

24. A regular pentagonal pyramid of side of base 24 mm and axis 60 mm long stands on its base on HP with one of the sides of the base parallel to VP and nearer to it. A square cut out of an 15 mm side is drilled through it such that its axis is parallel to HP and perpendicular to VP. The axis of the cut out intersects the axis of the pyramid at a distance of 15 mm from the base. The faces of the cut out are equally inclined to HP. Develop the lateral surfaces of the pyramid with the cut out.

25. A Hexagonal pyramid of 25 mm side of base and axis 60 mm long stands vertically with a base edge parallel to VP. A cylindrical slot of 32 mm diameter is drilled through the pyramid in such a way that the axis of the slot is perpendicular to VP. The center of the slot is 20 mm above the base and 10 mm away from the axis of the pyramid. Draw the development of the hexagonal pyramid with the slot formed on it.

DEVELOPMENT OF OBJECTS

26. Draw the development of the objects shown below (Fig. 16.82 to Fig. 16.85):