The total area of a cube is expressed by A(x) = 24x^2+24x+6. What is the volume of this cube?

1 Answer
Mar 2, 2018

8x3+12x2+6x+1

Explanation:

I'm going to assume you meant the surface area is given by A(x).

We have A(x)=24x2+24x+6

The formula for the surface area of a cube is given by 6k2, where k is the length of a side.

We can say that:

6k2=24x2+24x+6

k2=4x2+4x+1

k2=(2x+1)2

k=2x+1

So the length of a side is 2x+1.

On the other hand, V(x), the volume of he cube, is given by k3.

Here, k=2x+1

So we can say:

V(x)=k3=(2x+1)3

V(x)=(2x+1)2(2x+1)

V(x)=(2x+1)(4x2+4x+1)

V(x)=8x3+12x2+6x+1

So the volume of this cube is given by 8x3+12x2+6x+1