SOLUTION: a billiard ball is inscribed in a plastic cubical box having a volume of 2744 mm^3. what is the ratio of the billiard ball to that of the volume of the plastic cubical box

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Question 727397: a billiard ball is inscribed in a plastic cubical box having a volume of 2744 mm^3. what is the ratio of the billiard ball to that of the volume of the plastic cubical box
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The diameter of the ball is the same as the width of the box, and 2 times the radius.
The formula for volume of a sphere says that a ball of the radius
r has a volume of
V%28ball%29=%284%2F3%29%2Api%2Ar%5E3
A cube-shaped box of inside width 2r has an inside volume of
V%28box%29=%282r%29%5E3=8r%5E3
The ratio of the volumes is
V%28ball%29%2FV%28box%29=%284%2F3%29%2Api%2Ar%5E3%2F8r%5E3 --> V%28ball%29%2FV%28box%29=%284%2F3%29%2Api%2F8 --> V%28ball%29%2FV%28box%29=highlight%28pi%2F6%29
The sizes of ball and box do not matter.
As long as the ball fits tightly in the box, and the box is cube-shaped, the ratio is the same.

NOTE:
If you are curious, 2744mm%5E3=%2814mm%29%5E3 and that would make the diameter of your billiard ball 14mm.
That is way too small, marble size.
I did not use a calculator to find
root%283%2C2744%29=14
I just divided 2744 by 2, by 2, by 2, and by 7 to get 49 and realize that the prime factorization is
2744=2%5E3%2A7%5E3
so I knew that 2744=2%5E3%2A7%5E3=%282%2A17%29%5E3=14%5E3