Lesson 23T ~ Similar Solids
Name__________________________________________
Period______
Date____________
Determine if each pair of solids is similar. Write each ratio as a fraction.
1.
a. Ratio of the lengths:
10
b. Ratio of the widths:
5
4
c. Ratio of the heights:
2
4
8
d. Are the ratios all the same?
Yes
No
e. Are the prisms similar?
Yes
No
6
2.
a. What is the ratio of the radii?
8
b. What is the ratio of the heights?
8
c. Are the ratios the same?
Yes
No
d. Are the cylinders similar?
Yes
No
12
Circle the correct answer.
3. The scale factor between Solid A and Solid B is 3 : 4. What is the ratio between their heights?
A. 3 : 4
B. 9 : 16
C. 27 : 64
4. The scale factor between Solid T and Solid Y is 1 : 2. Identify their area ratio.
A. 1 : 2
B. 1 : 4
C. 1 : 8
5. The scale factor between Solid Q and Solid M is 2 : 5. Identify the area ratio.
A. 2 : 5
B. 4 : 25
C. 8 : 125
6. The ratio between the diameters of two similar cylinders is a : b. What is the volume ratio
between the two cylinders?
A. a : b
©2008 SMC Curriculum
B. a² : b²
C. a³ : b ³
Oregon Focus on Surface Area and Volume
7. Two similar prisms have a scale factor of 1 : 3. The small prism has a volume of 250 mm³. Find
the volume of the large prism.
a. Find the volume ratio.
a³ : b³
→
1³ : 3³
→
b. Write the volume ratio as a fraction.
c. Which ratio below can be used to find the volume of the large prism?
1 250

3
x
or
1
250

27
x
d. Set the cross products equal to one another.
e. What is the volume of the large prism?
8. A large wooden board has an area of 200 in². A small wooden board is similar to the large one.
The ratio of their lengths is 2 : 1. Find the area of the small board.
a. Find the ratio of their areas.
b. Write a proportion to find the area of the small board.
c. Find the area of the small board.
9. Two cylinders have a scale factor of 3 : 2. The surface area of the small cylinder is 43 ft². Find
the surface area of the large cylinder.
©2008 SMC Curriculum
Oregon Focus on Surface Area and Volume