Circular cone with height 24 and radius 6 is placed on circular face on a table. It is then cut by a horizontal plane...

Question

A circular cone with height 24 and radius 6 is placed on its circular face on a table. It is then cut by a horizontal plane, which is parallel to the circular base and passes through the midpoint of the height. The volume of the lower part of the cone can be written as A*PI.

What is the value of A?

Answer 1

The radius of the cone will reduce linearly from the Base to the mid section proportionately with the associated height. Therefore at the mid section the radius of the upper cone will be 3 units.

So required volume will be just the difference between the volume of the 2 cones
Ie.,

((pi/3)*r1^2*h1) - ((pi/3)*r2^2*h2)
Here r1= 6, h1 = 24, r2 = 3, h2 = 12.
Therefore we get the answer as = 252*pi