SOLUTION: I have a homework question. its something along these lines. "Billy has a box that is 20x40x30 in. he wants to fit the biggest ball he can in there, what percent of the box

Question 873887: I have a homework question.
its something along these lines.
"Billy has a box that is 20x40x30 in. he wants to fit the biggest ball he can in there, what percent of the box will this ball take up"
I know the volume of the sphere must be equal to or the same as the box, but I don't know how to do the rest of the problem.
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
The 20 unit dimension is a restriction on the diameter of the ball. Radius of the ball can therefore be up to r=10.

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
The diameter of the ball can be only 20 in r=10
Volume of sphere = (4/3) pi*r^3
=(4/3)*pi*10^3
=4188.80 in^3
Volume of box = 20*30*40=24000
percent volume taken up = (4188.80/24000)*100
17.45%
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