A hemisphere of lead of radius 7cm is cast into a right circular cone of height 49 cm. What would be the radius of base?

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

Vol of hemisphere
=2/3*22/7*r*r*r
=2/3*22/7*7*7*7.......................(i)
now ,
Vol of cone
=1/3*22/7*r*r*h
=1/3*22/7*r*r*49....................(ii)
as both of their volumes would be same,
therefore,
(i)=(ii)
2/3*22/7*7*7*7=1/3*22/7*r*r*49
simplify it,
r=Sqrt14
Ans:Radius of base of cone is Sqrt14 cm