Suppose cube A is 10 cm along each edge and cube B is 5 cm along each edge. What is the relationship of the volume of cube A to that of cube B?

To determine the relationship of the volume of cube A to that of cube B, we start by calculating the volumes of both cubes using the formula for the volume of a cube, which is ( V = s^3 ), where ( s ) is the length of an edge.

For cube A:

• The length of each edge is 10 cm.

• The volume is calculated as ( V_A = 10^3 = 1000 ) cubic centimeters.

For cube B:

• The length of each edge is 5 cm.

• The volume is calculated as ( V_B = 5^3 = 125 ) cubic centimeters.

Now, to find the relationship between the volumes:

• The ratio of the volume of cube A to that of cube B is ( V_A : V_B = 1000 : 125 ).

Performing the division for the ratio, we simplify ( \frac{1000}{125} = 8 ). This indicates that the volume of cube A is 8 times larger than the volume of cube B. Therefore, the correct relationship is that cube A has eight times the volume of cube B.

This illustrates how the cube's volume increases with the cube of its edge length.