Question

A company is moving large equipment in boxes in the shapes of cubes that hold 2000 cubic feet. The company needs to move these boxes by placing them on square platforms. The square base of the cube must entirely sit on the square platform. The square platforms have side lengths that only come in whole foot lengths. What is the smallest whole foot length that could be used for the square platforms? Justify.

Answer 1

45ft

Explanation:

To get smallest whole foot length that could be used for the square platforms, we will use the formula for calculating the volume of a square as shown:

Volume = L³ where:

L is the length of the cube

Given

Volume of the cubes = 2000ft³

.substitute

2000 = L³

L³ = 2000

Cube root both sides

(³√L)³ = ³√2000

L = 44.72ft

L ≈ 45ft

Hence the smallest whole foot is 45ft