Exercise [Sections of Solids]

EXERCISE

Sections of Prisms

1. A square prism having a base with 40 mm side and 60 mm long axis is on HP with an edge of the base perpendicular to VP. It is cut by a horizontal section plane bisecting the axis. Draw the front view and sectional top view.

2. A right pentagonal prism side of base 35 mm and height 60 mm lies on one of its triangular faces upon ground such that its axis is parallel to VP. A section plane parallel to HP cuts the axis at its mid point. Draw the front view and sectional top view of the prism.

3. A right regular hexagonal prism, side of base 30 mm and height 65 mm lying on one of its rectangular faces on HP, keeping the axis perpendicular to VP. A section plane parallel to HP cuts the solid at a height of 35 mm above the resting surface. Draw the front view and the sectional top view of the prism.

4. A cube with 40 mm long edges is resting on HP on one of its faces with a vertical face inclined at 30° to VP. It is cut by a section plane perpendiular to HP, parallel to VP and passing through a point 10 mm away from the axis. Draw its sectional front viw and sectional top view.

5. A Hexagonal prism having a base with 25 mm side and 70 mm axis long is resting on a corner of its base in HP and axis inclined at 60° to HP and parallel to VP. It is cut by a horizontal section plane which divides the prism into two equal halves. Draw its sectional top view and front view.

6. A pentagonal prism having a base with a 30 mm side and a 60 mm long axis is resting on a face on HP with its axis making 30° with VP. It is cut by a horizonal section plane passing through a point 10 mm below the top longer edge. Draw the front view and sectional top view. 

7. A triangular prism of base 50 mm side and axis 66 mm long has its base on the ground and its one rectangular face is parallel to VP. It is cut by a plane perpendicular to VP inclined at 60° to HP and passing through a point on the axis 20 mm below the top end. Draw the front view, sectional top view and an auxiliary plan view of the sectioned solid showing the true shape of section.

Sections of Pyramids

8. A square pyramid having a base with a 45 mm side and 70 mm long axis is resting on its base in HP with all the sides of the base equally inclined to VP. Draw its sectional top view, sectional side view and true shape of the section when it is cut by a section plane

i) Perpendicular to the VP bisecting the axis.

ii) Inclined at 45° to HP, and

iii) Inclined at 60° to HP.

9. A Hexagonal pyramid having base with a 25 mm side and a 70 mm long axis, rests on a triangular face in HP, with its axis parallel to VP. It is cut by a plane whose H.T makes an angle of 30° with the reference line and bisects the axis such that the apex is removed. Draw its sectional front view and obtain true shape of the section.

10. A pentagonal pyramid side of base 40 mm and 60 mm height rests with its base on HP. One of the edges of its base is perpendicular to VP. A section plane perpendicular to VP and inclined at 40° to HP bisects the axis. Draw the sectional top view and true shape of the section.

11. A Hexagonal pyramid of base side 30 mm and height 70 mm stands on the ground on its base with one side of the base perpendicular to the VP. It is cut by a vertical plane inclined at 30° to VP and passing through a point 10 mm away from the vertex. Draw topview, sectional front view and true shape of the section.

12. A pentagonal pyramid having a base with a 30 mm side and a 70 mm long axis is resting on its base in HP with an edge of the base parallel to VP. A horizontal section plane cuts the pyramid at a distance of 30 mm from the base. Draw its sectional views and determine the true sveshape of the section. 

13. A pentagonal pyramid has its base on the ground and the edge of the base nearer and parallel to VP. A vertical section plane, inclined at 45° to VP, cuts the pyramid at a distance of 10 mm from the axis. Draw the top view, sectional front view and true shape of the section.

14. A triangular pyramid side of base 45 mm and axis 65 mm long rests with its base on HP such that an edge of the base is parallel to and 18 mm in front of VP. A cutting plane inclined at 60° to HP and perpendicular to VP, bisects the axis of pyramid. Draw the top and profile views beni showing the section.

Sections of Cylinder

15. A cylinder with 50 mm diameter and 70 mm long axis is resting on its base on HP. It is cut by a section plane inclined at 45° to HP and perpendicular to VP such that the plane bisects the axis. Draw its front view, sectional top view and true shape of the section.

16. A cylinder with a 50 mm base diameter and a 70 mm long axis, is resting on its base on HP. It is cut by a section plane perpendicular to VP, the V.T of which cuts the axis at a point distant 20 mm from the top end of the axis and makes an angle of 45° with the reference line. Draw its front view sectional top view and another top view on an Auxiliary inclined plane parallel to the section plane.

17. A cylinder of 50 mm diameter and axis 80 mm long lies with one of its generators on HP such that its axis is inclined at 45° to VP. A section plane parallel to VP bisects the axis of the cylinder. Draw the top and sectional front views.

18. A cylinder is resting on its base upon HP. It is cut by a plane inclined at 60° to HP cutting the axis at a point 25 mm from the top. If the diameter of the cylinder is 50 mm and length is 60 mm, draw the projections of the sectioned cylinder and the true shape of section.

Sections of Cone

19. A cone with a 60 mm base diameter and a 70 mm long axis is resting on its base on HP. It is cut by a plane making 45° with HP and bisecting the axis. Draw front view, sectional top view and true shape of the section.

20. A cone with a 60 mm base diameter and a 70 mm long axis is resting on its base on HP. It is cut by a plane passing through a point, 25 mm below the apex and is parallel to one of the extreme generators. Draw its sectional top view and obtain true shape of the section. 

21. A cone with a 60 mm base diameter and a 70 mm long axis, rests on one of its generators in HP with its axis parallel to VP. It is cut by a plane inclined at 60° to HP, bisecting the axis. Draw its sectional top view and true shape of the section.

22. A cone with 60 mm base diameter and 70 mm long axis is resting its base on HP. It is cut by a section plane whose H.T makes an angle of 60° with the reference line and passes through a point that is 20 mm away from the axis. Draw its sectional front view and obtain true shape of the section.

23. A cone of 70 mm base diameter, axis 70 mm long is resting on its base on HP. It is cut by a vertical plane, the H.T of which makes angle of 30° with the reference line and is 15 mm away from the axis. Draw the sectional front view and the true shape of section, if the apex is retained after cutting the solid.

Sections of Sphere

24. A sphere of 70 mm diameter is cut by a section plane perpendicular to the V.P and inclined at 55° to the HP in such a way that the true shape of the section is a circle of 45 mm diameter. Draw its front view and sectional top view.

25. A sphere with a 70 mm diameter is kept on the H.P. It is cut by an Auxiliary Inclined Plane in such a way that the top view of the cut surface is an ellipse having major and minor axes 50 mm and 30 mm long respectively. Draw the front view, sectional top view and true shape of the section.