Volume Ratios of Similar Solids

The video tutorial explains how to find the volumes of similar solids using scale factors. It begins with a review of similar figures and introduces the concept of scale factors for perimeters, areas, and volumes. The tutorial then provides step-by-step examples of calculating the scale factor and using it to find the volume of similar solids, including cylinders, prisms, and pyramids. The key takeaway is that the volume ratio of similar solids is the cube of the scale factor.

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