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

• Jun 19th 2013, 08:25 AM
zaco519
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
• Jun 19th 2013, 09:07 AM
ebaines
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?
• Jun 19th 2013, 10:01 AM
HallsofIvy
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 $\displaystyle s\sqrt{3}$ and that is the diameter of the circumscribing sphere.