Question

The amount of paint that David needs to cover a cube is directly proportional to the surface area. If David can completely cover a cube of side length 2 feet with exactly 16 quarts of paint, how big a cube (in terms of edge length in feet) can David cover with 169 quarts of paint?

Answer 1

The cube must be 21.125 feet long.

Explanation:

David can completely cover a cube of side length equal to 2 feet, using 16 quarts of paint.

With this we make a conversion factor:

`(2)/(16)` feet/quarts = 0.125 feet/quarts

This means that with each quart of paint you can paint a 0.125-foot long cube

We need to know how big is the length of a cube that can be covered with 169 quarts of paint

Then we use the conversion factor found earlier

`\169quarts * (2pies)/(16quarts) = 21.125 feet.`

The cube must be 21.125 feet long.