I am learning how to write algebraic expressions.

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The volume of the cube is equal to four times the area of one of its faces. (There is a picture of a cube with one side - x in.) What is the volume of the cube?      Volume: ____________in 3

Oct 8th, 2015

Hi! Thanks for working with me on this question!

To find the volume of a cube, you should multiply the base times the width times the height.

For a cube, all of the sides are the same, so you just get x^3 for the volume.

If you want to find the area of one of the faces, you will notice that a face on the cube is a square. Area of a square is found by multiplying length times width. For this square, the area is x^2.

I would think about the first sentence as a math statement, and translate it:

The VOLUME of the cube is EQUAL to FOUR TIMES the AREA of one of its faces.

V = 4 * A

We know V and A, so plug those in:

x^3 = 4x^2

There are a couple of ways to finish the problem and find what x equals. One is to move all terms to one side:

x^3 - 4x^2 = 0

Then factor:

x^2(x - 4) = 0

Then set each "piece" to zero:

x^2 = 0     and     x - 4 = 0

Then solve each piece for x:

x = 0         and      x = 4

It doesn't make sense for the side length of the cube to be 0, so you know that x has to be 4.

The other way to solve the original equation only works for this problem because x can't be zero (since the side length of the cube can't be zero).

Remember we had x^3 = 4x^2 ?

You can divide both sides of the equation by x^2 (since you know x can't be zero, it's okay to divide by x)

so then you would have x = 4.

Now, remember you need to find the volume of the cube, so you will have to actually find what x^3 is, or what 4^3 is.

4x4x4 = 64

So your answer is 64 in^3.

I hope this helps you move forward on the problem! Let me know if you need any more clarification!
Oct 8th, 2015

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