Unit 11: Volume of all Types of Solids
8. right rectangular prism
Find the volume of the given
figure. Leave answers in terms
of π, when applicable.
16. square pyramid
1. right cylinder
9. right rectangular prism
17. square pyramid
10. right rectangular prism
2. right cylinder
18. right triangular prism
3. right cylinder
11. right cone
19. square pyramid
4. right cylinder
12. oblique cone
20. right triangular prism
5. right cylinder
13. right cone
21. sphere
6. right cylinder
14. oblique cone
22. sphere
7. right rectangular prism
15. right cone
23. sphere
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24. Frank owns a sandwich shop
27.
and he needs to build a cement
ramp for handicapped access. A
model of the ramp is shown
below. It is in the shape of a
triangular prism with right
triangle bases. If each cement
bag makes 5,040 cubic inches of
cement, how many bags are
needed to make the ramp?
A local ice & water store is changing
their snow-cone cups. Right now
the cups are cone shaped with a base
diameter of 4 inches. They are 6
inches tall and have a volume of 25.1
in3. The new containers will be
cylinders with a base diameter of 3
inches and a height of 4 inches (see
diagram). How much more or less
ice will the new container hold?
Current Cup:
Diameter = 4 inches
Height = 6 inches
Volume = 25.1 in3
25. An excavation company uses fill
dirt as a temporary ramp for its
trucks at a worksite. The ramp
has the shape of a triangular
prism, with a right triangle for a
base (see drawing). If a truck
carries 50 cubic feet of dirt, how
many truckloads of dirt will be
required to make the ramp?
New Cup:
Diameter = 3 inches
Height = 4 inches
28.
The manager of the local theatre is
considering changing the popcorn
containers. Right now popcorn is
sold in rectangular bags whose
dimensions are 2” by 3” by 8”. The
volume of the bags is 48 in3. The
new container would be in the shape
of a right cone with a base diameter
of 4” and a height of 9”.
How much more or less popcorn
will the new container hold?
Current Container:
Length = 3 inches
Width = 2 inches
Height = 8 inches
Volume = 48 in3
26. A storage tank in the shape of a
cylinder has a diameter of 40
feet, and the height of the tank
is 16 feet. How many pounds of
corn can the tank hold if 1
pound takes up approximately
0.157 cubic feet of space?
Round your answer to the
nearest pound.
29. If the scale factor of two similar
cylinders is 3:5, what will be the
ratio of the volumes?
30. The scale factor of two spheres
is 2:3 and the volume of the
smaller is 36π m3. What is the
volume of the bigger sphere?
31. Two similar cubes have volumes
of 27ft3 and 216ft3. What is the
scale factor of these two cubes?
32. Two similar pyramids have a
scale factor of 2:5. If the smaller
pyramid has a volume of 400 in3,
what is the volume of the larger
pyramid?
33. If the edge of a cube is increased
by 6 times, what effect will it
have on the volume?
34. If the radius of a sphere is
doubled, what effect will it have
on the volume?
35. If the edge of a cube is increased
by 7 times, what effect will it
have on the volume?
New Container:
Diameter = 4 inches
Height = 9 inches
ANSWERS
1). 226.08 cm3
13). 94.2 cm3
25). V=5000 ft 3 100 truckloads
2). 2.355 ft3
14). 226.08 ft3
26). V=20096 ft3  128000 lbs
15). 141.3 cm3
27). V=28.26 in3  3.16 in3 more
4). 49.455 cm3
16). 50 m3
28). V=37.68 in3  10.32 in3 less
5). 100.48 cm3
17). 432 cm3
29). 27:125
18).
30). 121.5π m3 (Use volume ratio 8:27)
7). 40 inches3
19). 150 km3
31). 1:2 (reduced from 3:6)
8). 60 inches3
20).
32). 6250 in 3 (use volume ratio 8:125)
9). 60 inches3
21). 113.04 cm3
33). 216 times larger
10). 216 inches3
22). 381.51 inches3
34). 8 times larger
11). 200.96 inches3
23). 7234.56 m3
35). 343 times larger
3). 62.8 m
3
6). 98.125 inches
12). 157 m3
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3
24). V=20160 in3  it will take 4 bags
© Mastery Mathematics