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?

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Answer 1 · 2016-12-19T15:19:01

31.42 sq units.

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.