Surface Area and Volume Ratios of Similar Solids

Front

What is the relationship between the linear scale factor and the area ratio of similar shapes?

Back

The area ratio is the square of the linear scale factor.

Front

If a triangle's linear scale factor is 3, how many times larger is its area?

Back

9 times larger.

Front

What is the surface area ratio of similar 3D shapes?

Back

The surface area ratio is the square of the linear scale factor.

Front

How do you find the volume ratio of similar solids?

Back

Cube the linear scale factor.

Front

If the linear scale factor is 5:6, what is the ratio of the areas?

Back

25:36.

Front

If the zoom factor is 2:9, what is the ratio of the volumes?

Back

8:729.

Front

What happens to the area when the linear dimensions of a shape are doubled?

Back

The area increases by a factor of 4.

Front

What is the formula for the volume of a cube?

Back

Volume = side^3.

Front

If the linear scale factor is 1:2, what is the ratio of the volumes?

Back

1:8.

Front

What is the relationship between the surface area and volume ratios of similar solids?

Back

Surface area ratio is squared; volume ratio is cubed.