Find the relationship describing the volume (V) of a cube as a function of the length of the diagonal going through the cube (d). and evaluate it for a diagonal length of d = 1.2.

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- Sep 29th 2010, 10:15 AMchoy777Find volume of a cube as a function of diagonal length.
Find the relationship describing the volume (V) of a cube as a function of the length of the diagonal going through the cube (d). and evaluate it for a diagonal length of d = 1.2.

- Sep 29th 2010, 01:11 PMArchie Meade
- Sep 30th 2010, 11:03 AMdeadmanLost
I got lost how did it end up over root3 cubed

- Sep 30th 2010, 11:34 AMArchie Meade
After applying Pythagoras' theorem twice, we get... "internal diagonal"=

where "x" is the length of a side of the cube.

The volume of the cube is

Since

then

which is the cube volume.

This allows us to express the cube volume as a function of the internal diagonal length.

The internal diagonal goes from the bottom right-corner of the base of the cube to the

top-left corner of the facing side,

or from the bottom left-corner to the facing side's top right-corner.

I'll be the first to admit that my sketch is not drawn well!

The sides should appear to be the same lengths.