=3D=3D>When one gets the derivative of the volume of a sphere with respec= t =3D=3D>to its radius, one gets the surface area. Obviously, this is not =3D=3D>the case with cubes. Does anybody know why this is true with =3D=3D>spheres?
But it IS the case with cubes. =
Write V =3D (2r)^3, where r is the perpendicular distance from =
the origin to a face. =
dV/dr =3D 24r^2 which is the surface area.
You need to express the volume in terms of one parameter "r" where r must (I think) be perpendicular to the surface. This is so that you could have gotten the volume by =
integrating S(r) dr.
You just have to choose the right coordinates. =
I suspect that the sphere & the cube are the only solids with enough symmetry to play this trick, but maybe it =
can be done with any of the regular solids. =