Geometry Worksheet: Shapes Lesson 4
Similar Solids/Shapes Test Review
Name: __________________________ No: ________
Round all answers to
TWO decimal places.
1. Find the volume and surface area of each figure.
a) Given: Square Pyramid
b) Given: Right Cone
25 ft
13 in
15 ft
12 in
Volume = __________ Surface Area = __________ Volume = __________ Surface Area = __________
c)
d)
8 cm
15 cm
18 cm
4 cm
Volume = __________ Surface Area = __________ Volume = __________ Surface Area = __________
e)
f)
3m
10 cm
Volume = __________ Surface Area = __________ Volume = __________ Surface Area = __________
2. The ratio of the lengths of two similar solids is 4 : 7.
a) What is the ratio of their perimeters?
b) What is the ratio of their areas?
c) What is the ratio of their volumes?
3. Two similar spheres have volumes of 8𝜋 cubic
feet and 216𝜋 cubic feet. What is the ratio of the
surface area of the smaller sphere to the surface
area of the larger sphere?
Surface Area Ratio: __________
4. Two similar rectangular prisms have
corresponding lengths of 5 centimeters and 8
centimeters. What is the ratio of the volume of the
smaller rectangular prism to the volume of the
larger rectangular prism?
Volume Ratio: __________
5. Two similar cylinders have a scale factor of 3 : 8.
The smaller cylinder has a surface area of 70𝜋 square
meters. Find the surface area of the larger cylinder.
6. How much paper is needed to make a label for
a can of beans with a diameter of 9.5 cm and a
height of 12.5 cm? (The label has no overlap.)
Surface Area = __________
Amount of Paper = __________
7. The dimensions of rectangular prism A are 8 m
x 12 m x 4 m. The dimensions of rectangular prism
B are 9.6 m x 14.4 m x 4.8 m. Are the two
rectangular prisms similar? (Show work to support your
8. How much empty space is in the can of tennis
balls pictured? The tennis balls are touching each
other and the top, bottom, and sides of the can.
The tennis balls each have a radius of 2 inches.
answer.)
Circle: YES NO
9. Two water tanks are similar cylinders with
diameters of 8 feet and 18 feet. If it takes 3200
gallons of water to fill the larger tank, how many
gallons of water are needed to fill the smaller tank?
Empty Space = __________
10. The figure consists of a cylinder and a
hemisphere as shown. Find the volume of the
figure.
Volume = __________
18 ft
Smaller Tank = __________
11. A scoop (spherical in shape) of ice cream with
a diameter of 8 centimeters is placed in an ice
cream cone with a diameter of 10 centimeters and
a height of 12 centimeters. Is the cone large
enough to hold all the ice cream if the entire scoop
melts? If yes, how much extra space would be left
in the cone? If not, how much ice cream would
spill out?
32 ft
12. Given: The two solids are similar.
𝑉 = 64𝜋 ft3
𝑉 = 27𝜋 ft3
a) Find the scale factor of the larger solid to the
smaller solid.
b) Find the scale factor of the surface areas of the
smaller solid to the larger solid.
13. If the length, width, and height of a
rectangular prism are tripled, how many times
larger is the volume of the new prism to the
volume of the original prism?
14. If the diameter and height of a cylinder are
doubled, how many times larger is the surface area
of the new cylinder to the surface area of the
original cylinder?
__________
__________
15. A cylindrical water tank has a radius of 5
inches and a height that is two times its radius.
Find the volume of the water inside the tank when
16. The volume of a rectangular prism is 520 cubic
inches. A similar rectangular prism has dimensions
that are four times those of the original rectangular
prism. Find the volume of the larger rectangular
prism.
the tank is
3
4
full.
Volume = __________
Volume = __________
17. A student is comparing two similar cones. The
surface area of the smaller cone is 0.09 times that
of the larger cone. The volume of the smaller cone
is 108 cm3. Find the volume of the larger cone.
18. The radii of two similar spheres are in the ratio
of 7 : 9. If the lateral area of the larger sphere is
486 in2, find the lateral area of the smaller sphere.
Lateral Area = __________
Volume = __________
19.
20.
6 ft
30 ft
9 ft
3 ft
52 ft
32 ft
Volume = __________ Surface Area = __________ Volume = __________ Surface Area = __________
21. The volume of a cylinder is 726𝜋 ft3. If its
height is 6 feet, find its radius.
22. Find the area of the shaded region given that
the figure is a square.
Radius = __________
Shaded Area = __________
12 in
12 in
23. Find the area of the shaded figure.
24. Find the area of the shaded region.
Area = __________
Shaded Area = __________
3 ft
3 ft
11 ft
4 in
12 ft
10 in
25. A cylinder has a volume of 80𝜋 m3 and a
height of 5 meters. Find the surface area of a
sphere with a radius equal to that of the cylinder.
26. A cone has a lateral area of 52𝜋 cm2 and a
circular base with an area of 169𝜋 cm2. Find the
slant height of the cone.
Surface Area = __________
Slant Height = __________