Question

A box with an open top has a square base and four sides of equal height. The volume of the box is 96 ft³. The height is 2 ft greater than both the length and the width. If the surface area is 112 ft²​, what are the dimensions of the​ box?

Answer 1

Dimension of box = 4 ft x 4 ft x 6 ft

Explanation:

Let a be the base side of square, and h be the height.

The height is 2 ft greater than both the length and the width.

h = a + 2

The volume of the box is 96 ft³.

Volume = Base area x Height = a² x h = a² x (a+2)

a² x (a+2) = 96

We will get a = 4 ft

Dimension of box = 4 x 4 x (4+2) = 4 ft x 4 ft x 6 ft