SOLUTION: If diagnol of a cube is 12 cms then volume is in cubic cms?

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Question 1028361: If diagnol of a cube is 12 cms then volume is in cubic cms?
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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If diagonal of a cube is 12 cm then volume is in cubic cms?
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If a cube has the edge of the length "a", its diagonal (a true "3D diagonal") has the length a%2Asqrt%283%29.

So, you are given a%2Asqrt%283%29 = 12.

Then a = 12%2Fsqrt%283%29,

and the volume is a%5E3 = %2812%2Fsqrt%283%29%29%5E3 = %2812%2A12%2A12%29%2F%283%2Asqrt%283%29%29 = %2812%2A12%2A4%29%2Fsqrt%283%29 = %2812%2A12%2A4%2Asqrt%283%29%29%2F3 = 12%2A4%2A4%2Asqrt%283%29 = 192%2Asqrt%283%29 cm%5E3.


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


A cube has a diagonal. I don't know what a "diagnol" is.

If the edge of a cube is represented by , then the diagonal of one face is . This is from the Pythagorean Theorem, .

Then one edge of the cube, measuring and the diagonal of a face, measuring , form the legs of another right triangle where the diagonal of the cube is the hypotenuse. So using the Pythagorean Theorem again:



So, if your diagonal measures , then



Solving and rationalizing the denominator



The volume of the cube is the measure of the edge cubed, so:



You can do the rest of the arithmetic.

John

My calculator said it, I believe it, that settles it