Question

A rectangular solid and a cube are of equal volume. If the rectangular solid is 20 centimeters long, 5 centimeters wide, and 10 centimeters high, what is the length, in centimeters, of an edge of the cube?

Answer 1

10 centimeters.

Explanation:

First, we need to remember what's the formula to get the volume of a rectangular solid and a cube.

The volume of the first equals:

Volume = Length x Width x Height

While the volume of the cube is:

`Volume = a^(3)` where a is the edge.

We are given the measures of the rectangular solid so we can calculate its volume:

`Volume= (20)(5)(10)=1000` cubic cms.

Now, we know that both the volume of the rectangular solid and the cube are the same so we will use this information to calculate the edge of the cube.

`1000=a^3 \\\sqrt[3]{1000} =\sqrt[3]{a^3} \\10=a`

Thus the length of an edge of the cube is 10 centimeters