SOLUTION: what is the volume of the empty space left when three tennis balls with a diameter of 3 inches are packed into a cylindrical container that is 9 inches tall with the same diameter

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Question 451381: what is the volume of the empty space left when three tennis balls with a diameter of 3 inches are packed into a cylindrical container that is 9 inches tall with the same diameter as the tennis ball?
Answer by kingme18(98) About Me  (Show Source):
You can put this solution on YOUR website!
To find the volume of the leftover space, you need to find the total volume (volume of the cylinder) and the volume of the balls (spheres), then subtract to find everything IN the cylinder and OUTSIDE the balls. Note that for both the cylinder and the spheres, the radius is 1.5 since the diameter is 3.
The formula for the volume of a cylinder is +pi%2Ar%5E2%2Ah+. This is approximately +3.14%2A1.5%5E2%2A9=63.585. The volume of a sphere is +4%2F3%2Api%2Ar%5E3. In your case, this is about 4%2F3%2A3.14%2A1.5%5E3=14.13. However, there are 3 balls. Since each one is 14.13 cubic inches, we'll multiply by 3 and get 42.39. We can now subtract the total minus the balls: 63.585-42.39=21.195 cubic inches.