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 $16$ . If the volume of the solid is $75 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-11-20T16:56:29

$(15 pi)/4$

If 'r' is the radius of the cone, its volume would be $1/3 pi r^2 h= 1/3 pi r^2 *12=4 pi r^2$

Since 'r' is also the radius of the cylinder, its volume would be $pi r^2 h= 16pir^2$

Total area of the solid is thus $4pi r^2 +16 pi r^2 = 20 pi r^2$

Thus $20 pi r^2 = 75 pi$

$r^2=75 /20=15/4$

Area of the base of the cylinder would be $pi r^2= (15 pi)/4$

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 16 16 . If the volume of the solid is 75 pi75 pi, what is the area of the base of the cylinder?