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
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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
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.
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