Question

A cone of radius 10cm is divided into two parts by a plane parallel to its base through the mid point of its height. compare the volumes of the two parts

Answer 1

As the cone is divided into two equal parts by the axis so, AQ = AP/2
with the help of similarity theory,
QD / PC = AQ / AP
so, QD / PC = 1/2
so, rdius of QD = PC/2 = R/2
now,the volume of frustum = 1/3πR²H - 1/3π(R/2)²(H/2)
                                                = 1/3πR²H*7/8
compare the two parts in cone
1st is the volume of small cone and 2nd the volume of frustum
i.e. (1/3π(R/2)²(H/2))/(1/3πR²H*7/8) = (1/8)/(7/8)=1/7