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Two congruent cones with radius 12 cm and height 12 cm are enclosed within a cylinder. The base of each cone is a base of the cylinder, and the height of the cylinder is 24 cm. What is the number of cubic centimeters in the volume of the cylinder not occupied by the cones? Express your answer in terms of \(\pi\).

 Jun 27, 2019

Volume occupied by TWO cones =   2    x  pi r^2  h/3

     = 2   * pi (12^2) (12/3) = 1152 pi    cm^3


Volume of cylinder = pi r^2 h

   = pi 12^2 (24) = 3456 pi    cm^3



Subtract the volume of the cones from the volume of the cylinder

     3456 pi -1152 pi= 2304 pi  cm^3                  = 7238.23 cm^3

 Jun 27, 2019

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