Question

Find the perimeter around the bottom of the following cube-shaped box with a volume of 40x^4

Answer 1

The perimeter of the bottom of the cube-shaped box is equal to
`8\sqrt[3]{5}\cdot x^(4)/(3)` units.

How to determine the perimeter of the bottom of a cube-shaped box

Herein we must determine the perimeter of the bottom of a cube-shaped box. The volume and perimeter formulae are described below:

Volume of a cube

V = l³

Where V is in cubic units.

Perimeter of the bottom of a cube:

p = 4 · l

Where l is the side length, measured in units.

Then, we must determine the perimeter of the cube. First, calculate side length:

`l = \sqrt[3]{40\cdot x^4}`

`l = 2\sqrt[3]{5}\cdot x^(4)/(3)`

Second, compute the perimeter of the bottom of the cube:

`p = 8\sqrt[3]{5}\cdot x^(4)/(3)`