SOLUTION: A ball is placed snugly into the smallest possible box that will completely contain the ball. What percentage of the box is filled by the ball?

Question 292024: A ball is placed snugly into the smallest possible box that will completely contain the ball. What percentage of the box is filled by the ball?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let the side of box be x
the volume of box will be x^3
The diameter of the ball will be x
so radius will be x/2
the volume of ball will be 4/3 * pi*(x/2)^3
= 4/3* pi*x^3/8
4/3*1/8 +pi*x^3
1/6 *pi^x^3
the ratio of the volume of ball to box will be
1/6 * pi* x^3 / x^3
=1/6*3.14 *100
52.33 % of the volume of box

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