OK this problem we want to express the edge length of a cube as a function of the cubes diagonal length D. So if that diagonal length here is D we want to be able to figure out what the side length is. So we have a diagonal D. We also have this red line here that if we could figure out this red line here with the base here, we'd have a right triangle. So when we look at this, we want to think about what length this red triangle is the diagonal. Well, it's the diagonal of a face. And so if we thought about looking at this diagonal here, we'd have this face and we would know that this face in relationship to the sides. Let's currently call the side X&X. This side here is going to be X * sqrt 2 by Pythagorean theorem if that's X ^2 of two and this is X. Now when we look at the diagonal a ^2 + b ^2 = C ^2 so we get X ^2 plus X sqrt 2 ^2 has to equal d ^2. So when we multiply this out and add it together we get X ^2 + 2 X squared equaling d ^2. So D is going to be X square roots of three. So if we wanted the length, express the edge length of a cube as a function of the cubes diagonal. So we're actually going to get the X equaling D over the cube root of 3. Then from there we're going to figure out the surface area. We have six sides, so we're going to figure out the area of one side and multiply it by 6. And then we're going to do the volume. So the surface area, because it's a cube, is 6 times the area of the side. I'll use a for area of the side, the little subscript. And then the volume is just length times width times height, or in this case the side times side times side.