I am learning how to write algebraic expressions.

Tutor: None Selected Time limit: 1 Day

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

Did you know? You can earn $20 for every friend you invite to Studypool!
Click here to
Refer a Friend
Oct 8th, 2015
Oct 8th, 2015
Feb 26th, 2017
Mark as Final Answer
Unmark as Final Answer
Final Answer

Secure Information

Content will be erased after question is completed.

Final Answer