A solid consists of a cone on top of a cylinder with a radius equal to the cone. The height of the cone is 3 and the height of the cylinder is 12 . If the volume of the solid is 25 pi, what is the area of the base of cylinder?

1 Answer
Nityananda
Sep 12, 2016

25/13 pi sq unit

Explanation:

We know the vol of a cone is 1/3 pi r^2 h1 cu unit where h1 is height of cone and r is radius of cone. we also know the vol of cyl is pi r^2 h2 cu unit where h2 is height of cyl and radius is same as cone
So as per question, 1/3 pi r^2 h1 + pi r^2 h2 = 25 pi
or, pi r^2(1/3 h1+h2) = 25 pi
or, r^2(1/3 * 3 + 12) = 25
or, r^2 = 25/13

Now the area of base of cyl is pi r^2 = 25/13 pi sq unit

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