Question

The number of one-inch cubes that will fit into a box that is 6 inches wide and one inch tall is 54. how long is the box?

Answer 1

54 ÷ 6 = 9

the box is 9 inches long

Answer 2

9 inches long is the box.

Explanation:

Volume of a cube is given by:

`\text{Volume of a cube} = s^3` where, s is the side of the cube

Volume of a box(V) is given by:

`V = lwh` .....[1]

where

l is the length , w is the width and h is the height of the box respectively.

As per the statement:

The number of one-inch cubes that will fit into a box that is 6 inches wide and one inch tall is 54.

Volume of one box =
`1^3 = 1` in.

then;

Volume of 54 box = 54 inches.

It is also given:

w = 6 inches and h = 1 inch

Substitute in [1] we have;

`54 = l \cdot 6 \cdot 1`

⇒
`54 =6l`

Divide both sides by 6 we get;

`9 = l`

or

`l = 9 in.`

therefore, 9 inches long is the box.