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)   (Show Source): You can put this solution on YOUR website!
.
If diagonal of a cube is 12 cm then volume is in cubic cms?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

If a cube has the edge of the length "a", its diagonal (a true "3D diagonal") has the length .

So, you are given  = .

Then a = ,

and the volume is  =  =  =  =  =  =  .


Answer by solver91311(24713)   (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

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