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 9 and the height of the cylinder is 6 6. If the volume of the solid is 45 pi45π, 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^2hV=13πr2h

Volume of a cylinder is given by V = pir^2hV=πr2h

1/3pi(r)^2(9) + r^2(6)(pi) = 45pi13π(r)2(9)+r2(6)(π)=45π

3r^2pi + 6r^2pi = 45pi3r2π+6r2π=45π

9r^2pi = 45pi9r2π=45π

9r^2 = (45pi)/pi9r2=45ππ

9r^2 = 459r2=45

r^2 = 5r2=5

r = sqrt(5)r=5

The area of a circle is given by r^2pir2π

(sqrt(5))^2pi(5)2π

=5pi5π

The area of the base of the cylinder is 5pi5π

Hopefully this helps!