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 42 and the height of the cylinder is 10 . If the volume of the solid is 240 pi, what is the area of the base of the cylinder?

1 Answer
Dec 19, 2016

31.42 sq units.

Explanation:

Let the radius = r unit.

We know volume of cone = 1/3 pi.r^2.h cubic units

rArr 1/3 pi. r^2. 42 = 14. pi. r^2 cubic units.

And the volume of cylinder = pi.r^2.h

rArr pi. r^2. 10 cubic units.

Now as per questions :-

14.pi.r^2 + 10.pi.r^2 = 240. pi

rArr pi.r^2.(14+10) = 240. pi

rArr r^2 = [240. pi]/[24. pi]

rArr r^2 = 10

Now base of the cylinder = pi. r^2 sq units

rArr 22/7. 10 = 31.42 sq units.