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

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Answer 1 · 2018-03-02T04:12:40

#8x^3+12x^2+6x+1#

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

We have #A(x)=24x^2+24x+6#

The formula for the surface area of a cube is given by #6k^2#, where #k# is the length of a side.

We can say that:

#6k^2=24x^2+24x+6#

#k^2=4x^2+4x+1#

#k^2=(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 #k^3#.

Here, #k=2x+1#

So we can say:

#V(x)=k^3=(2x+1)^3#

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

#V(x)=(2x+1)(4x^2+4x+1)#

#V(x)=8x^3+12x^2+6x+1#

So the volume of this cube is given by #8x^3+12x^2+6x+1#