Blah! Finding a relatinship between volume and a diagonal

[Stevo11]

1. The problem statement, all variables and given/known data

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

I seriously dont know where to start, I'm taking Biology, but I have to take calculus as well and I'm seriously awful at math and have no clue how to start this problem :frown:

[Fellowroot]

Look up the volume of a cube formula.

V=LWH, L=length, W=width, H=height

Now, note that this is a cube. In math when you read or hear words like cube, bells should be going off telling you that this implies that all the sides are going to be of equal distance.

So.

L=W=H

V=L^3

Now for the diagonal going through the cube, I'm going to assume that the line spans the maximum distance that it can inside the cube, from one corner to its opposite diagonal corner. For this distance you can use the Pythagorean theorem twice.

Once for a triangle that is flat on the floor with the longest side as the diagonal from corner to corner of the base of the square. The next will use the longest side of the previous triangle as the base and now the longest side of the new triangle will be the like the 3-D diagonal path of the line inside the cube. (it may take a few seconds to see this)

Call each side L and express the volume in terms of it after using the Pythagorean theorem twice. After you have that then plug in for L=1.2