Geometry
Volume WS
Name_____________________________________
NOTE: Area (equilateral triangle) =
1
4
s2 3
Area (hexagon) = 6 14 s 2 3
Find the volume of the prism or cylinder. If necessary, give your answer in terms of  .
1.
2.
3.
4.
5.
6.
Find the volume of the sphere. Give your answers in terms of  .
7.
8.
9.
Solve for the variable using the given measurements. The prisms and the cylinders are
right. Round to one decimal place.
10.
11.
12.
Find the volume of the cone or regular pyramid. If necessary, round your result to two
decimal places.
13.
14.
15.
16.
17.
18.
19. How much extra space will you need to fill the inside of a box with dimensions 44 cm x 44
cm x 44 cm after placing a bowling ball inside with a radius of 21.8 cm?
20. A rubber shell filled with air forms a rubber ball. The shell’s outer diameter is 65 mm, and
its inner diameter is 56 mm. Find the volume of rubber used to make the ball. Round to the
nearest cubic cm.
21. To complete a construction job, a contractor needs 145 more cubic yards of concrete. If there
remains a conical pile of concrete mix measuring 36 feet in diameter and 12 feet high, is
there enough concrete still on the job site to finish the job? Explain your reasoning.
22. The limestone blocks from which an ancient pyramid was made weigh about 2 tons per cubic
yard. Find the approximate weight of the pyramid having a square base of length 250 yards
and a height of 150 yards.
Find the volume of the solid. Each prism is right. Round your result to one decimal place.
23.
24.
Solve the following practice SAT problems. Show all work!
25. What is the height of a right cylinder with radius 5 inches and volume 150π inches3?
A.
B.
C.
D.
E.
5 inches
6 inches
7 inches
8 inches
9 inches
26. What is the radius of a right cone with height 5 cm and volume 90π cm3?
A.
B.
C.
D.
E.
3 2 cm
2 3 cm
6 cm
9 cm
18 cm
27. The area of the base of a cylinder is 100π m2. The volume of the cylinder is 900π m3. What
is the height of the cylinder?
A.
B.
C.
D.
E.
9m
10 m
11 m
12 m
13 m
28. A cone has radius twice the height. The height of the cone is equal to the radius of a sphere.
Which of the statements is true about the ratio between the volume of the cone and the
volume of the sphere?
A.
B.
C.
D.
E.
2:1
1:2
4:1
1:4
1:1
29. The volume of a rectangular prism is 1080 cm3. The ratio : w : h  2 : 4 : 5 . What is the
surface area of the prism?
A.
B.
C.
D.
E.
2052 ft2
1368 ft2
1080 ft2
684 ft2
342 ft2
30. What is the volume of a cube whose surface area is 96?
A.
B.
C.
D.
E.
16 2
32
64
125
216
31. The length, width, and height of a rectangular solid are in the ratio of 3:2:1. If the volume of
the box is 48, what is the total surface area of the box?
A.
B.
C.
D.
E.
27
32
44
64
88
32. The base area of a cylinder is 16π m2. A plane
cuts the cylinder in half forming the rectangle at
the right. If the volume of the cylinder is 240π m3
what is the area of the rectangle?
33. A box is constructed by cutting 3-inch squares
from the corners of a square sheet of cardboard, as
shown in the diagram at the right, and then folding
the sides up. If the volume of the box is 75 in3,
find the number of square inches in the area of the
original sheet of cardboard.