A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $12$ and the height of the cylinder is $28$ . If the volume of the solid is $16 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-06-07T13:24:39

Area of base of cylinder is $pi/2$ .

Let the area of the base of cylinder be $A$ , as its height is $28$ units

volume of cylinder is $28xxA=28A$

volume of cone of height $12$ units will be $1/3xxAxx12=4A$ units

hence total volume is $28A+4A=32A=16pi$

Hence, Area of base of cylinder is $16pi/32=pi/2$ .

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is 12 12 and the height of the cylinder is 28 28 . If the volume of the solid is 16 pi16 pi, what is the area of the base of the cylinder?