SOLUTION: A ball with a volume of 250 centimetres cubed is placed in a box. The box is shaped like a cube and the ball is touching the centre of each face of the cube (on the inside). Calcul

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Question 987995: A ball with a volume of 250 centimetres cubed is placed in a box. The box is shaped like a cube and the ball is touching the centre of each face of the cube (on the inside). Calculate the volume of empty space inside the cube
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A ball with a volume of 250 centimetres cubed is placed in a box.
The box is shaped like a cube and the ball is touching the centre of each face of the cube (on the inside).
Calculate the volume of empty space inside the cube.
:
Find the radius of the ball using the volume formula
4%2F3pi%2Ar%5E3 = 250
multiply both sides by 3
4%2Api%2Ar%5E3 = 750
r%5E3 = 750%2F%284%2Api%29
r%5E3 = 59.6831
r = 59.6831%5E%281%2F3%29
r = 3.908 cm is radius
then
2(3.908) = 7.816 cm is the diameter, this is also the length of the side of the box
7.816^3 = 477.465 cu/cm is the volume of the box
:
477.465 - 250 = 227.465 cu/cm is the empty space around the ball in the box