Question

The height of a cube furniture piece is x+10 in. if the volume of the cube is x^3+1000 cu. in, how much area does each face of the cube have?

Answer 1

from the given question the correct answer is:

The area of each face of the cube ${ (x^2 - 10x + 100)}/{6}$ is square inches.

Given:

The height of a cube furniture piece = (x+10) inches.

The volume of the cube = (x³ + 1000) cubic inches.

To find:

The area of each face of the cube

Solution: given that

,The volume of a cube is

by the formula (side)³.

The volume is given in the form of a³ + b³ = (a + b)(a² - ab + b²).

,

Total surface area of the cube = volume/height

$= \frac{(x^3 + 1000)}{(x + 10)}\\\\ =\frac{ (x + 10)(x^2 - 10x + 100)}{(x + 10)}\\\\ = (x^2 - 10x + 100) square inches.$

 We know that a cube has six faces.

Hence, the area of each face of the cube is square inches.