Ratios of Cube Dimensions and Properties

The video tutorial explains the relationship between the ratios of lengths, surface areas, and volumes of similar solids, using cubes as examples. It demonstrates how to calculate these ratios and generalizes the correlation between them. The tutorial shows that the ratio of lengths is to the power of one, the ratio of surface areas is to the power of two, and the ratio of volumes is to the power of three. This understanding helps in determining one ratio if the others are known.

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

• 6 cm

• 10 cm

• 8 cm

• 4 cm

What is the volume of the larger cube?

• 800 cm³

• 500 cm³

• 1000 cm³

• 64 cm³

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

• 2:5

• 8:125

• 4:10

• 16:25

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

• 4³:10³

• 2:5

• 2³:5³

• 2²:5²

What is the total surface area of the smaller cube?

• 96 cm²

• 84 cm²

• 64 cm²

• 100 cm²

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

• 16:100

• 8:125

• 2:5

• 4:25

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

• 4:10

• 8:125

• 2³:5³

• 2²:5²

What is the power relationship for the ratio of lengths?

• Power of 1

• Power of 4

• Power of 2

• Power of 3

What is the power relationship for the ratio of surface areas?

• Power of 4

• Power of 1

• Power of 2

• Power of 3

What is the power relationship for the ratio of volumes?

• Power of 1

• Power of 2

• Power of 4

• Power of 3