# Thread: If a cube has the volume of 1000 then what is the smallest sphere that could be circu

1. ## If a cube has the volume of 1000 then what is the smallest sphere that could be circu

If a cube has the volume of 1000 then what is the smallest sphere that could be circumscribed around it?
Is it 500√2 or 500√3
how did you do it

2. ## Re: If a cube has the volume of 1000 then what is the smallest sphere that could be c

Are you looking for the radius of the smallest spehere? First determine the length of each side of the cube. Then the spehere will have a radius that reaches from the center of the cube to each corner, so use Pythagorus to determine that length. By the way, neither of your answers are correct - perhaps the volume isn't 1000 but rather 1,000,000,000?

3. ## Re: If a cube has the volume of 1000 then what is the smallest sphere that could be c

Equivalently, the length of a diagonal of a cube of side s has length $s\sqrt{3}$ and that is the diameter of the circumscribing sphere.