Question

Two boxes have the same volume. One box has a base that is 2 inches by 2 inches. The other box has a base that is 4 inches by 4 inches.

How many times as tall is the box with the smaller base?

Answer 1

It is 4 times as tall

Explanation:

Answer 2

4 times as tall.

Explanation:

Volume of the box with the smaller base = 2*2* h1 = 4h1 where h1 is its height.

Similarly the volume of the larger base box = 4*4 * h2 = 16h2 with height h2.

So the ratio of their volumes is 16h2 / 4h1 = 4h2 / h1.

Now the volumes are equal so 4h2 = h1.

Therefore h2 = h1/4 so h1 = 4h2.

The box with the smaller base is 4 times as tall as the other box.