Question

A cone of radius 10 cm is divided into two parts by drawing a plane through the mid point of its axis parallel to the base . Compare the volume of two parts.

Answer 1

     V = (1/3) r²h
a plane parallel to base and passing through midpoint of its height divides the cone in two parts: a smaller cone with height h/2 and radius r/2 whose volume is V' and a truncated cone whose volume is V'' = V - V'
V' = (1/3)  (r/2)² (h/2) = (1/24)  r²h
V'' = (1/3) r²h - (1/24)  r²h = (7/24) r²h

V''/V' = ((7/24) r²h)/((1/24)  r²h) = 7

V'' = 7 V'