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 $42$ $42$ and the height of the cylinder is $10$ $10$ . If the volume of the solid is $240 π$ $240 pi$ , 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 = $\frac{1}{3} π . r^{2} . h$ $1/3 pi.r^2.h$ cubic units

$\Rightarrow \frac{1}{3} π . r^{2} . 42 = 14 . π . r^{2}$ $rArr 1/3 pi. r^2. 42 = 14. pi. r^2$ cubic units.

And the volume of cylinder = $π . r^{2} . h$ $pi.r^2.h$

$\Rightarrow π . r^{2} . 10$ $rArr pi. r^2. 10$ cubic units.

Now as per questions :-

$14 . π . r^{2} + 10 . π . r^{2} = 240 . π$ $14.pi.r^2 + 10.pi.r^2 = 240. pi$

$\Rightarrow π . r^{2} . (14 + 10) = 240 . π$ $rArr pi.r^2.(14+10) = 240. pi$

$\Rightarrow r^{2} = \frac{240 . π}{24 . π}$ $rArr r^2 = [240. pi]/[24. pi]$

$\Rightarrow r^{2} = 10$ $rArr r^2 = 10$

Now base of the cylinder = $π . r^{2}$ $pi. r^2$ sq units

$\Rightarrow \frac{22}{7} . 10 = 31.42$ $rArr 22/7. 10 = 31.42$ sq units.

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 4242 and the height of the cylinder is 1010 . If the volume of the solid is 240π240 pi, what is the area of the base of the cylinder?