7. Frustum of solids
When any solid is cut by a plane which is parallel
to the base, then it is called a frustum of a solid
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8. Truncated Solids
When any solid is cut by a plane which is inclined
to the base then it is called a truncated solid.
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9. Problems on CASE 1 - Pyramids
1. A square pyramid of base edge 30 mm and altitude 60 mm rests on
one of its base edges on the HP with its axis inclined at 30o to
HP and parallel to VP. Draw the plan and elevation.
2. Draw the plan and elevation of a hexagonal pyramid of base 40 mm
and altitude 70 mm when it is resting on HP on one of its
corners, with its axis inclined at 40o to HP and parallel to VP.
3. A right pentagonal pyramid side of base 30 mm and height 60 mm
rests on one of its base edges on HP; the base being lifted up
until the highest corner in it is 40 mm above HP. Draw the
projections when the edge on which it rests is made perpendicular
to VP (AU – Tirunelveli)
4. Draw the plan and elevation of a cone when it is resting on HP on
one of its point of its circumference. Its base is making an angle of
30o to HP and its axis is parallel to VP. Take diameter of cone = 50
mm and altitude 70 mm. www.arpradeep.tk
10. Problems for Practice CASE 1 - Pyramids
5. Draw the front and top view of a square pyramid of side 35 mm and
axis length 65 mm, is resting on HP with one of its corners. Its axis is
making an angle of 40o with HP and parallel to VP
6. A hexagonal pyramid of side 30 mm and height 60 mm rests on HP
with one of its base edges. Its axis inclined at 45o to HP and parallel
to VP. Draw the plan and elevation.
7. A pentagonal pyramid of base 35 mm and axis 65 mm long rests on
HP with one of its base corners. The base containing the resting
corner makes on angle of 50o with HP. Its axis is parallel to VP. Draw
the plan and elevation.
8. A rectangular pyramid of size 25mmx35mm rests on HP with one of
its shorter base edges. The base containing the resting base edge
makes an angle of 50o with HP. Its axis is parallel to VP. Draw the front
and top views. (UQ)
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11. Problems on CASE I - Prisms
1. A hexagonal prism of base side 30 mm and axis length 60 mm
rests on HP on one of its base edges with its axis inclined at
60o to the HP and parallel to the VP. Draw its top and front views.
2. Draw the projections of a pentagonal prism of base side 20 mm
and axis length 50 mm when it rests on the ground on one of
its corners of the base and the axis inclined at 35o to the
ground and parallel to VP.
3. A cylinder of diameter 30 mm and axis length 50 mm is lying on
HP on a point so that its axis is inclined at 45o to the HP and
parallel to VP. Draw its top and front views.
4. A rectangular prism of size 30mm x 40 mm rests on HP on one of
its larger edges of the base on the HP. Its axis is inclined at
40o to HP and parallel to VP. Draw its projections.
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12. Problems for Practice CASE 2 - Prisms
5. A square prism of base side 35 mm and axis length 60 mm rests on
one of its base edges on the HP, with the rectangular face
containing the base edge is inclined at 30o to HP and parallel to VP.
Draw the front and top views.
6. Draw the projections of a hexagonal prism of side 30 mm and height
65 mm rests on ground on one of its corners, with the base
containing the resting corner making an angle of 40o to HP. Its axis
is parallel to VP.
7. Draw the plan and elevation of a pentagonal prism of side 35 mm and
height 60 mm rests on HP on one of its base edges, with its axis
inclined at 40o to HP and parallel to VP.
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13. Problems on CASE 2: Pyramids
1. Draw the projections of a square pyramid of base side 30 mm and
axis 50 mm when it is resting on HP on one of its base corners
with a base side containing the corner making 35o with the HP.
The axis is inclined at 30o to the VP and is parallel to the HP and
the vertex is away from the VP. (UQ)
2. A cone of base diameter 50 mm and axis length 60 mm is resting
on HP on a point on the circumference of the base with its axis
inclined at 40o to VP and parallel to HP. Draw its projections.
3. A hexagonal pyramid of base side 40 mm and axis length 55 mm is
resting on VP on one of its base edge with its axis inclined at
35o to VP and parallel to HP. Draw its projections.
4. A square pyramid of base side 35 mm and axis length 65 mm is
resting on VP on one of its triangular faces with its axis parallel
to HP. Draw its projections.
5. A pentagonal pyramid of base side 35 mm and axis length 65 mm
is resting on VP on one of its triangular faces with its axis
parallel to HP. Draw its projections.
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14. Problems on CASE 2: Pyramids
6. A cone of base 40 mm diameter and axis length 65 mm is
resting on one of its base point with its axis parallel to
HP and inclined at 40o to VP. Draw its projections.
7. A cone of base diameter 40 mm and axis length 60 mm is
resting on VP on one of its generators with its axis
parallel to HP. Draw its projections.
8. A cone of 15 mm radius and 70 mm height rests on the
ground on one its base circle points such that the
apex is 20 mm and the nearest base circle point is
50 mm infront of VP and the base is perpendicular to
HP. Draw the projections.
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15. Problems on CASE 2: Prisms
1. A square prism of base side 35 mm and axis length 60 mm lies on
the HP on one if its longer edges with its faces equally inclined to
the HP. Draw its projections when its axis is inclined at 30o to VP.
2. A square prism of base side 35 mm and axis length 60 mm is
resting on HP on one of its longer edges with its axis inclined
at 25o to VP. One of its faces containing the resting edge
inclined at 25o to HP. Draw its projections.
3. A pentagonal prism of base side 35 mm and axis length 65 mm is
resting on HP on one of its rectangular faces with its axis
inclined at 40o to VP. Draw the projections.
4. A cylinder of base 40 mm diameter and axis length 60 mm resting
on one of its generators on HP with its axis inclined at 45o to
VP. Draw its projections.
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16. Case 3:Freely Suspended by String
Formula to find centre gravity when the solid is
freely suspended by string:
1. For Pyramids, CG = 1/4th of the Axis length
2. For Prisms, CG = Half of the Axis length
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17. Freely suspended by a string
1. A hexagonal prism of side 30 mm and axis length 60 mm is freely
suspended by a string from one of its base corners with its axis
parallel to VP. Draw its projections.
2. A solid pentagonal pyramid of base side 25 mm is freely suspended
from a string attached to one corner of the base of the
pyramid. The string is held such that the apex of pyramid is just
touching the HP. The axis of the pyramid is parallel to VP. Draw the
projections of pyramid.
3. A cylinder of base side 40 mm and axis length 60 mm is freely
suspended by means of a string from one of its base point with
its axis parallel to VP. Draw its projections.
4. a cone of base side 40 mm and axis length 50 mm is freely
suspended by means of a string from one of its base point with
its axis parallel to VP. Draw its projections.
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18. CASE 4
Conditions: One of its triangular face on ground, one of
its generators on ground
1. A square pyramid of base side 60 mm and altitude 100 mm lies on
HP on one of its triangular faces with its axis parallel to the
VP. Draw its projections.
2. Draw the projections of a cone of base diameter 50 mm and axis
length 70 mm when it lies on ground on one of its generators
with the axis parallel to VP.
3. A hexagonal pyramid of base edge 40 mm and altitude 80 mm
rests on one of its triangular faces on HP, with its axis parallel
to VP. Draw its projections.
4. A square pyramid of base side 30 mm axis length 50 mm has one
of its triangular faces on VP and the axis parallel to and 25 mm
above HP. Draw its projections (UQ)
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19. Special Case 5: One triangular face is vertical
(or perpendicular to both HP and VP)
1. A hexagonal pyramid of base side 30 mm and altitude 75 mm
rests on HP on one of its base edges such that the triangular
face containing the resting edge is perpendicular to both HP
and VP. Draw its projections.
2. A pentagonal pyramid of base side 30 mm and altitude 70 mm is
resting on HP on one of its base edges such that the triangular
face containing the resting edge is perpendicular to both HP
and VP. Draw its projections.
3. Draw the projection of a cone of diameter 40 mm and height 70
mm lying on the ground on one of its base points with a
generator perpendicular to HP.
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20. Case 5: solid diagonal is vertical
6. A hexagonal pyramid of base side 30 mm and axis length
60 mm is resting on HP on one of its base corners with a
solid diagonal through that corner is perpendicular to HP.
Draw its projections and print the length of the diagonal
(UQ)
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21. UNIT IV - Section of Solids
Type
Condition of cutting
plane
Cutting Line Cutting Plane
1 Cutting plane parallel to
HP and Perpendicular to
VP
FV TV
2 Cutting plane parallel to
VP and Perpendicular to
HP
TV FV
3 Cutting plane inclined to
HP and perpendicular to
VP
FV TV
4 Cutting plane inclined to
VP and perpendicular to
HP
TV FV
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22. Section of solids – Type 1
1. A hexagonal pyramid of base side 30 mm and axis length 60 mm is
resting on HP on its base sides being perpendicular to VP. It is cut
by a plane perpendicular to VP and parallel to and 25 mm above
HP. Draw is elevation and sectional plan.
2. A square prism of side 30 mm and axis length 60 mm is resting on
HP on its base, so that one of its rectangular faces is inclined at 40O
to VP. It is cut by a section plane perpendicular to VP and
parallel to HP. The cutting plane is passing through mid point on
the axis of the prism. Draw the elevation and sectional plan.
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23. Section of solids – Type 2
1. A pentagonal pyramid, side of base 30 mm and axis 60 mm long
rests with its base on HP such that one of the edges of the base is
perpendicular to VP. A section plane perpendicular to HP and
parallel to VP cuts the pyramid at a distance of 20 mm from the
corner of the base nearer to the observer. Draw its top view and
sectional front view. (UQ)
2. A square prism with a base side of 40 mm and an axis length of 65
mm resting on its end on the HP. All the vertical faces are equally
inclined to the VP. A vertical sectional plane passing through the
mid points of two adjacent sides of the prism cuts the prism.
Draw the top view and sectional front view. (UQ)
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24. Section of solids – Type 3
1. A pentagonal pyramid of base side 20 mm and altitude 55 mm rests
on its base on HP, with one of base edges perpendicular to VP. It is
cut by a plane inclined at 50O to base. The cutting plane meets the
axis at 15 mm above the base. Draw the front view, sectional top
view and true shape of section
2. A cone is placed on the HP with its base of diameter 40 mm and 60
mm altitude. It is cut by a plane inclined at 45O to HP and
perpendicular to VP and bisects the axis. Draw the sectional plan
and true shape of section.
3. A Square pyramid of base side 35 mm and axis length 70 mm rests on
hp on one of its base edge perpendicular to VP. It is cut by a section
plane 45o inclined to HP and perpendicular to VP. The section plane
passing through a point at a distance of 30 mm from apex. Draw the
front view, sectional top view and true shape of section.
4. A cone of base diameter 40 mm and axis length 60 mm is resting on
HP on its base. It is cut by a plane perpendicular to VP and parallel
to a contour generator and is 10 mm away from it. Draw the front
view, sectional top view and true shape of section. (UQ)
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25. Section of solids – Type 3
5. A cylinder of 40 mm diameter and height 65 mm rest on its base on
HP. It is cut by a section plane inclined at 45O to HP and
perpendicular to VP. The section plane passes through a point on the
axis at a height of 55 mm from the base. Draw the front view,
sectional plan and true shape of section.
6. A square prism of base side 25 mm and axis length 60 mm is lying on
HP on one of its base side inclined at 25O to VP. It is cut by a plane
inclined at 40O to HP and perpendicular to VP and bisecting the axis
of the prism. Draw its front view, sectional top view and true shape
of section.
7. A hexagonal prism of base side 25 mm and axis 65 mm rest on its
base on HP. It is cut by a plane inclined at 45O to HP and
perpendicular to VP. The section plane passes through a point on the
axis at a height of 50 mm from the base. Draw the front view,
sectional plan and true shape of section.
8. A cone of base diameter 50 mm and axis length 60 mm is resting on
HP on its base. Its cut by a plane perpendicular to VP and inclined
at 75O to HP and is passing through the apex of the cone. Draw its
front view, sectional top view and true shape of section. (UQ)
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26. Section of Solids – Type 4
1. A hexagonal pyramid of base side 25 mm and axis 70 mm long is
resting with two of the sides perpendicular to VP. It is cut by a
section plane perpendicular to horizontal and 10 mm away from
the axis. Draw the top and sectional front view and true shape of
section.
2. A cone of base diameter 50 mm and axis length 60 mm is resting on
HP on its base. It is cut by a plane inclined at 40O to VP and
perpendicular to HP that cuts the cone at a distance of 10 mm
from axis and infront of it. Draw the top view, sectional front
view and true shape of section.
3. A pentagonal pyramid of base 30 mm and axis 60 mm is resting on
HP on its base with a base side parallel to VP. It is cut by a plane
inclined at 45o to VP and perpendicular to HP and is 12 mm away
from the axis. Draw the sectional top view and true shape of
section.
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27. Section of solids – Type 5 ( True shape is
given)
1. A cone of base 40 mm diameter and axis 70 mm long is resting on
its base on HP. It is cut by a section plane, so that the true shape
of section is an ellipse of major axis 50 mm and minor axis 25
mm. Determine the inclination of section of the section plane with
HP and draw the projections of solid.
2. A square prism of 32.5 mm side and 102mm height is lying on its
base on HP such that the edges of the base are equally inclined to
VP. The prism is cut by a section plane passing through the mid
point of the axis such that the true shape of section is a rhombus
of diagonals of 93 mm and 46 mm. Determine the inclination of
the section plane.
3. A square pyramid of base side 30 mm and axis 50 mm lies on the
HP on its base with its base edges equally inclined to VP. It is cut
by a plane perpendicular to VP and inclined to HP cuts the base
also, such that the true shape is an isosceles triangle of base side
20 mm and altitude 45 mm. Draw the projection and find the
inclination of the section plane.
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28. Section of solids – Type 6 ( cutting plane
perpendicular to both HP and VP)
1. A cone of base diameter 50 mm and axis length 75 mm is resting on
HP on its base. It is cut by a plane perpendicular to both HP and
VP and is 10 mm to the left of the axis. Draw the front view, top
view and true shape of section.
2. A square pyramid of base side 30 mm and axis length 60 mm is
resting on HP with a side of base inclined at 30O to VP. It is cut by
a plane perpendicular to both HP and VP and 10 mm away from
the axis. Draw top view, front view and sectional top view.
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