Emmy used one-centimeter cubes to build a larger cube. The edges of Emmy's cube are 3 centimeters long. Tim has a cube-shaped box with edges that are 3 times as long as the edges of Emmy's cube. How much larger in volume is Tim's box than Emmy's cube?

Tim's box volume is 27 times greater than Emmy's.

Step-by-step explanation:

The volume of a cube is given by the following expression:

volume = l³

Since Emmy's cube have a 3 centimeters long edge, then it's volume is:

volume1 = 3³ = 27 cm³

On the other hand Tim's cube has an edge that is 3 times as long as Emmy's, so it's 9 centimeters long. Therefore it's volume is:

volume2 = 9³ = 729 cm³

The relation between the volume is given by:

ratio = volume2/volume1 = 729/27 = 27

Tim's box volume is 27 times greater than Emmy's.