An aquarium is in the shape of a cube. The aquarium can hold between 4096 cubic inches and 8000 cubic inches of water. What are the possible side lengths of the aquarium?

The possible side lengths are either 16 inches or 20 inches

Step-by-step explanation: The aquarium is in the shape of a cube which suggests that, all dimensions (length, width and height) are equal.

If it can hold 4096 cubic inches of water, then the volume of water in it can be calculated as follows;

Volume = L x W x H

Knowing that all three dimensions are the same the formula can be re-written as;

Volume = L³

4096 = L³

Add the cube root sign to both sides of the equation

∛4096 = ∛L³

16 = L

Also if it can hold up to 8000 cubic inches of water, then the volume of water in it can be calculated as;

Volume = L³

8000 = L³

Add the cube root sign to both sides of the equation

∛8000 = ∛L³

20 = L

Therefore, if the aquarium can hold between 4096 and 8000 cubic inches of water, then the side lengths are either 16 inches or 20 inches