Volume Ratios of Similar Solids

What is the relationship between the scale factor and the ratio of the volumes of similar solids?

• The ratio of the volumes is the scale factor.

• The ratio of the volumes is the scale factor cubed.

• The ratio of the volumes is the scale factor to the power of four.

• The ratio of the volumes is the scale factor squared.

If the scale factor between two similar solids is 3, what is the ratio of their volumes?

• 27

• 9

• 6

• 3

Given two similar cylinders with a scale factor of 2, if the volume of the smaller cylinder is 45π cubic units, what is the volume of the larger cylinder?

• 720π cubic units

• 360π cubic units

• 180π cubic units

• 90π cubic units

In the example of similar square prisms, if the base edge of prism A is 4 inches and the base edge of prism B is 6 inches, what is the scale factor?

• 2/3

• 3/2

• 6/4

• 4/3

If the scale factor between two similar square prisms is 3/2, what is the ratio of their volumes?

• 3/2

• 6/4

• 27/8

• 9/4

Given two similar solids with a scale factor of 3/4, if the volume of the smaller solid is 96 cubic meters, what is the volume of the larger solid?

• 108 cubic meters

• 72 cubic meters

• 54 cubic meters

• 40.5 cubic meters

In the example of similar pyramids, if the height of pyramid A is 6 inches and the height of pyramid B is 15 inches, what is the scale factor?

• 3/2

• 5/2

• 5/3

• 2/5

If the scale factor between two similar pyramids is 5/2, what is the ratio of their volumes?

• 25/4

• 5/2

• 125/8

• 10/4

Given two similar pyramids with a scale factor of 5/2, if the volume of the larger pyramid is 312.5 cubic inches, what is the volume of the smaller pyramid?

• 20 cubic inches

• 25 cubic inches

• 30 cubic inches

• 35 cubic inches

If the scale factor between two similar solids is 3, what is the ratio of their volumes?

• 9

• 6

• 27

• 3