Question

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

2 Times as tall with the small base

Answer 2

The volume of the box with base area
`A` and height
`h` is

`V=Ah`.

The volumes of the box with base area
`2*2` and with base area
`4*4` are the same. Let
`h_1,h_2` be the heights of the box with smaller base area and larger base area respectively. Then,

`image`.

Thus the height of the box with smaller base area is
`4` times that of the box with larger base area.