Cube's Volume

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Can someone please help me with this problem...

The volume of a cube is equal to four times the area of one of its faces. What is the volume of the cube if one of the lengths is x inches?

I'm not understanding why the answer is 64 cubic inches.

Thank you for your help!

Assume that the side of cube = x

Then

Volume of the cube V = x3

area of one face = x2

then

x3 = 4 * x2

Now solve for 'x' and then V.
 
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cube's volume is equal to 4 times the area of 1 of its faces.

[FONT=LearnosityMath, Helvetica Neue, Helvetica, Arial, sans-serif]The volume of the cube is equal to four times the area of one of its faces. What is the volume of the cube?[/FONT]

[FONT=LearnosityMath, Helvetica Neue, Helvetica, Arial, sans-serif]None of the values are provided. There is a picture of a cube with one of the edges marked x in. How do you find the volume if none of the values are provided? [/FONT]
 
How do you solve for x in this situation? Would you find the square root of 4x2

Assume that the side of cube =x2

Then

Volume of the cube V = x3

area of one face = x2

then

x3 = 4 * x2

Now solve for 'x' and then V.
 
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The catch here is that you only need one value to be provided, because you know it's a cube. In a cube, all side lengths are the same - in this case, they're the same unknown value x, so your volume will be a function of x, rather than a number.
 
But there are no values provided. This is how I set it up...
Volume=4(x*x)
V=4x*4x
V= 16x^2
V=4(16x^2)
V=64in^3

I ended up with the correct answer but don't know if I went about it right.
The catch here is that you only need one value to be provided, because you know it's a cube. In a cube, all side lengths are the same - in this case, they're the same unknown value x, so your volume will be a function of x, rather than a number.
 
That could be the correct process, and it's good that you arrived at the correct answer. But I'm hesitant to say for sure without seeing the supplied picture myself - it could just be a coincidence.
 
But there are no values provided. This is how I set it up...

Define your variable: Let x = the length of the edge of the cube

Volume=4(x*x) \(\displaystyle \ \ \ \ \ \ \ \)from the given information

V=4x*4x\(\displaystyle \ \ \ \ \ \ \ \)That's not equal to the expression immediately above.

V= 16x^2

V=4(16x^2)\(\displaystyle \ \ \ \ \ \ \ \)That's also not equal to the expression immediately above.


V=64in^3

I ended up with the correct answer but don't know if I went about it right.

\(\displaystyle V \ = \ 4x^2 \ \ \ and \ \ \ V \ = \ x^3 \) \(\displaystyle \ \ \ \ \ \) (from the volume of a cube equals its edge cubed)

Set \(\displaystyle \ \ x^3 \ \ equal \ \ to \ \ 4x^2, \ \ \) and solve for the positive value of x:

\(\displaystyle x^3 \ = \ 4x^2\)

\(\displaystyle x^3 - 4x^2 = 0 \)


Can you continue on this route?
 
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How do you solve for x in this situation? Would you find the square root of 4x2

No. Factor out the greatest common factor and continue.

\(\displaystyle x^3 - 4x^2 = 0\)

\(\displaystyle ?(? \ - \ ?) = 0\)
 
How do you solve for x in this situation? Would you find the square root of 4x2
The left side of the equation is some number x multiplied by itself three times . The right hand side of the equation is 4 times a number x multiplied by itself 2 times.

Fill in the squares with the same number.

\(\displaystyle \Huge_\Box * \Huge_\Box * \Huge_\Box = 4*\Huge_\Box * \Huge_\Box\)

Clearly that number is 4.
 
\(\displaystyle V \ = \ 4x^2 \ \ \ and \ \ \ V \ = \ x^3 \) \(\displaystyle \ \ \ \ \ \) (from the volume of a cube equals its edge cubed)

Set \(\displaystyle \ \ x^3 \ \ equal \ \ to \ \ 4x^2, \ \ \) and solve for the positive value of x:

\(\displaystyle x^3 \ = \ 4x^2\)
From this point I would note that x= 0 makes both sides 0 but that does not give a "cube".
If x is not 0, we can divide both sides by \(\displaystyle x^2\) to get x= 4.

\(\displaystyle x^3 - 4x^2 = 0 \)


Can you continue on this route?
 
Note to readers: The original poster for this thread, qcbrink, posted in reply to the following old thread. The two postings have now been joined.
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Originally Posted by sjsfan01Can someone please help me with this problem...

The volume of a cube is equal to four times the area of one of its faces. What is the volume of the cube if one of the lengths is x inches?

I'm not understanding why the answer is 64 cubic inches.


Thank you for your help!


Assume that the side of cube = x

Then

Volume of the cube V = x3

area of one face = x2

then

x3 = 4 * x2

Now solve for 'x' and then V.

x3 = 4 * x2

Since x\(\displaystyle \ne\)0 → divide both sides by x2. We get

x3/x2 = 4 * x2/x2

Leading to:

x = 4 in. → V = x3 → V = 43 → V = 64 cubic inches
 
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