Science a GoGo's Home Page Forums General Discussion General Science Discussion Forum a little problem with spears, i mean spheres

consider a sphere with 7cm radius.a cube is placed inside it in such a way that the 8 vertices of the cube touches the inner surface of the sphere[considering the sphere has almost no thickness]find the volume of the cube.

This is easy. Just note that the diameter of the sphere is the same as the diagonal of the cube.

and the answer would be....?

It is really quite obvious unless you are a biginner. I'll assume that you are and that you need some help. The thinking goes like this:

The diagonal of the cube is the same as the diamter of the enclosing sphere. Call this length d. If a cube has a side of length s, then

d^2 = 3s^2.

The volume V of a cube is give as

V = s^3.

Solve the first equation for s. That gives you

s = d/sqrt(3).

Use this in the second equation to arrive at

V = d^3/sqrt(3^3).

Since you know d this equation gives you V, which is what you want.

I'll leave the arithmetic for you to work out. Enjoy!