55. You have an empty cone and a cylinder filled with water. The cone has a diameter of 8 and a height of 9. The cylinder has a diameter of 10 and a height of 12. If you dump the water from the cylinder into the cone until it is filled, what volume of water will remain in the cylinder

  252π ≈ 791.7 cubic units

Step-by-step explanation:

The relevant volume formulas are:

  cone: V = 1/3πr²h

  cylinder: V = πr²h

  the radius is half the diameter

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The volume of the cone is ...

  V = 1/3π(4²)(9) = 48π . . . cubic units

The volume of the cylinder is ...

  V = π(5²)(12) = 300π . . . cubic units

The volume of water remaining in the cylinder after the cone is filled is ...

  cylinder volume - cone volume

  = 300π -48π = 252π ≈ 791.7 . . . cubic units