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 $18$ and the height of the cylinder is $36$ . If the volume of the solid is $420 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2018-04-01T13:51:29

$10pi$

Volume of cone $=pir^2h/3$

Volume of cylinder $=pi r^2h$

$:.pir^2h/3+pir^2h=420pi$

$:.pir^2*18/3+pir^2*36=420pi$

$:.pir^2(6+36)=420pi$

$:.42pir^2=420pi$

$:.42r^2=420$

$:.r^2=10$

$:.r=sqrt10$

Area of a circle $=pir^2$

$:.=pi(sqrt10)^2$

$:.=10pi$

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 18 18 and the height of the cylinder is 36 36 . If the volume of the solid is 420 pi420 pi, what is the area of the base of the cylinder?