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?

1 Answer
Apr 1, 2018

10pi

Explanation:

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