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 $200 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-07-10T10:50:09

The area of the base of the cylinder (which is a circle with radius $r$ ) $=pir^2=25pi/3sq.unit$ .

Suppose that the radius of cone $= r =$ that of cylinder.

Therefore, volume $V$ of the solid=volume of cone + that of cylinder

$=1/3*pi*r^2*$ (height of cone)+ $pi*r^2*$ (height of cyl.)

$=1/3*pi*r^2*42+pi*r^2*(10)$

$=14pir^2+10pir^2$

$:. V=24pir^2$

But we are given that $V=200pi.$

Therefore, $24pir^2=200pi rArr pir^2=200pi/24=25pi/3.............(1)$

Hence, the area of the base of the cylinder (which is a circle with radius $r$ ) $=pir^2=25pi/3$ sq.unit, by $(1).$

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 200 pi200 pi, what is the area of the base of the cylinder?