Download Area and Volume of Similar Solids Name

Ch 13 s4 Homework
Similar Figures & Solids
Name____________________________
For 1-3, are the solids similar? Support you answer.
1.
2.
12m
6m
4.
3m
5m
10m
m
2.5m
12m
2.5m
3.
10m
7m
5m
12m
5m
Prism A is similar to Prism B.
a. What is the similarity ratio of Prism A to Prism B?
13m
6m
Prism A
6.5m
Prism B
b. What is the ratio of the heights of Prism A to Prism B?
c. What is the scale factor of Prism A to Prism B?
10m
4m
d. What is the ratio of the surface areas of Prism A to Prism B?
e. What is the ratio of the volumes of Prism A to Prism B?
5.
Cylinder A is similar to Cylinder B. The radius of cylinder A is 27 ft, the radius of cylinder B is 12 ft.
a. What is the similarity ratio of Cylinder A to Cylinder B?
b. What is the ratio of the heights of Cylinder A to Cylinder B?
c. What is the scale factor of Cylinder A to Cylinder B?
d. What is the ratio of the surface areas of Cylinder A to Cylinder B?
e. What is the ratio of the volumes of Cylinder A to Cylinder B?
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Ch 13 s4 Homework
6.
The surface areas of two similar cones are 121 ft2 and 36 ft2.
a. What is the ratio of the lateral areas?
b. What is the similarity ratio of the large cone to the small cone?
c. What is the ratio of their radii?
d. What is the ratio of their volumes?
7. The ratio of the volumes of two spheres is 125:8.
a. What is the ratio of the surface areas?
b. What is the ratio of their radii?
8.
Mimi has two jewelry boxes that are similar cylinders. If the ratio of the radii is 5:7, what is the
ratio of the volume of the smaller cylinder to that of the larger cylinder?
9.
The surface areas of one face of two cubes are 49 ft2 and 100 ft2. What is the ratio of the
volume of the smaller box to that of the larger box?
10. The volumes of two similar triangular prisms are 343 ft3 to 216 ft3. What is the ratio of the
lateral area of the larger triangular prism to the smaller triangular prism?
11. A cereal box is a rectangular prism. If the area of the base is doubled and the height is not
changed, how many times greater will the volume be?
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Ch 13 s4 Homework
12. Cube A is similar to Cube B. The sides of Cube B are four times larger than the sides of Cube A.
a. What is the scale factor of Cube A to Cube B?
b. What is the ratio of the lateral areas of Cube A to Cube B?
c. What is the ratio of the surface areas of Cube A to Cube B?
d. What is the ratio of the volumes of Cube A to Cube B?
13. The radius of a small sphere is multiplied by a scale factor of 10 to produce a larger sphere.
Radius = r
Radius = 10r
a. What is the scale factor of the small sphere to the large sphere?
b. What is the ratio of the surface areas of the small sphere to the large sphere?
c. What is the ratio of the volumes of the small sphere to the large sphere?
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