SOLUTION: a ball is inscribed in a cubical box having a volume of 15, 625 mm cube. determine the volume of the empty space betwwen the ball and the cubical box

Question 612812: a ball is inscribed in a cubical box having a volume of 15, 625 mm cube. determine the volume of the empty space betwwen the ball and the cubical box
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the cube has a volume of 15,625 cubic millimeters.
each side of the cube is therefore equal to 25 millimeters because 25^2 = 15625.
since the sphere is inscribed in the box, this means that the diameter of the sphere is 25 millimeters which means that the radius of the sphere is equal to 12.5 millimeters (half the diameter).
the volume of a sphere is equal to 4/3 * pi * r^3 so the volume of the sphere is equal to 4/3 * pi * (12.5)^3 which is equal to 8181.230869 cubic millimeters.
the empty space in the box is equal to 15625 - 8181.230869 which is equal to 7443.769131 cubic millimeters.

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