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) (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
has a volume of
A cube-shaped box of inside width has an inside volume of
The ratio of the volumes is
--> -->
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, 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
I just divided 2744 by 2, by 2, by 2, and by 7 to get 49 and realize that the prime factorization is
so I knew that
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