Question

A closed box with a square base is to have a volume of 5400 cm3.

What should the dimensions of the box be if the amount of material used is to be minimum?

Answer 1

Since the base of the box is square, let's assume that each side of the base measures "x" cm. The height of the box will also be "x" cm, since it is a box with a square base.

The volume of the box is calculated by multiplying the length, width and height of the box. In this case, the volume is given as 5400 cm³:

Volume = length x width x height

5400 = x * x * x

5400 = x³

To find the value of "x", simply calculate the cube root of 5400:

x = ∛5400

x ≈ 17.32

So, to minimize the amount of material used, the dimensions of the box should be approximately 17.32 cm in length, 17.32 cm in width and 17.32 cm in height.

Explanation: