Question

A wooden box has a square base. The height of this box is 2 times the length of one side of the base. If the volume of the box is 128 cubic ft, what is the height of this box?

(E) 4 ft.
(F) 8 ft.
(G) 16 ft.
(H) 64 ft.

Answer 1

The height of the box is (F) 8 ft.

Explanation:

We know that a wooden box has a square base and that the height is 2 times the length of one side of the base. That can either be the length or the width of the box. The volume of the box is 128 cubic feet.

We're asked to find the height of the box.

Volume = l · w · h

128 = l · w · height which is twice the length of either the width or the length

but since it's a square base, it doesn't matter which side is the height twice of

128 ÷ 2 = 64

`\sqrt[3]{64}` = 4

4 × 4 = 16

128 ÷ 16 = 8

Length = 4, Width = 4 and height = 8