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

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- Jun 19th 2013, 08:25 AMzaco519If 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 - Jun 19th 2013, 09:07 AMebainesRe: 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?

- Jun 19th 2013, 10:01 AMHallsofIvyRe: 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 $\displaystyle s\sqrt{3}$ and that is the diameter of the circumscribing sphere.