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 9 and the height of the cylinder is 6 . If the volume of the solid is 45 pi, what is the area of the base of the cylinder?

1 Answer
May 5, 2016

Volume of a cone is given by V = 1/3pir^2h

Volume of a cylinder is given by V = pir^2h

1/3pi(r)^2(9) + r^2(6)(pi) = 45pi

3r^2pi + 6r^2pi = 45pi

9r^2pi = 45pi

9r^2 = (45pi)/pi

9r^2 = 45

r^2 = 5

r = sqrt(5)

The area of a circle is given by r^2pi

(sqrt(5))^2pi

=5pi

The area of the base of the cylinder is 5pi

Hopefully this helps!