Ratios in Similar Solids

The video tutorial explains the relationship between the dimensions of similar solids, focusing on cubes. It covers how to calculate and compare the volumes and surface areas of two cubes with different side lengths. The tutorial demonstrates that the ratio of the lengths, areas, and volumes of similar solids can be expressed as powers of the ratio of their corresponding lengths. This concept is generalized to apply to any similar solids, providing a method to find the ratio of volumes and surface areas from the ratio of lengths.

What is the side length of the smaller cube in the example?

• 4 cm

• 10 cm

• 6 cm

• 8 cm

What is the volume of the larger cube?

• 64 cm³

• 500 cm³

• 1000 cm³

• 800 cm³

What is the simplified ratio of the volumes of the two cubes?

• 4:10

• 16:25

• 8:125

• 2:5

How can the ratio of the volumes be expressed in terms of perfect cubes?

• 5³:6³

• 2³:5³

• 3³:4³

• 1³:2³

What is the total surface area of the smaller cube?

• 84 cm²

• 96 cm²

• 100 cm²

• 64 cm²

What is the simplified ratio of the surface areas of the two cubes?

• 4:25

• 16:36

• 8:125

• 2:5

How can the ratio of the surface areas be expressed in terms of perfect squares?

• 1²:2²

• 5²:6²

• 3²:4²

• 2²:5²

What is the power of the ratio for lengths in similar solids?

• 3

• 2

• 4

• 1

What is the power of the ratio for surface areas in similar solids?

• 4

• 3

• 2

• 1

What is the power of the ratio for volumes in similar solids?

• 2

• 3

• 1

• 4