Similar Figures and Area/Surface Area/Volume

Front

What is the ratio of the areas of two similar figures if the ratio of their corresponding side lengths is 2:5?

Back

The ratio of their areas is 4:25.

Front

If the area of triangle A is 54 and triangle B is 150, what is the scale factor of A to B?

Back

The scale factor of A to B is 3:5.

Front

What is the relationship between the ratio of the volumes of two similar solids and the ratio of their corresponding side lengths?

Back

The ratio of the volumes is the cube of the ratio of the side lengths.

Front

If the ratio of the volumes of two spheres is 64:27, what is the ratio of the lengths of their radii?

Back

The ratio of the lengths of the radii is 4:3.

Front

How do you find the scale factor of two similar figures?

Back

Divide the lengths of corresponding sides of the figures.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

If the side lengths of two similar figures are in the ratio 3:1, what is the ratio of their areas?

Back

The ratio of their areas is 9:1.

Front

What is the formula for the volume of a sphere?

Back

Volume = (4/3) * π * r^3.

Front

If the area of a rectangle is 60 square units and its length is 10 units, what is its width?

Back

Width = Area / Length = 60 / 10 = 6 units.

Front

What is the scale factor if the volume of a cube is increased from 1 cubic unit to 27 cubic units?

Back

The scale factor is 3:1.