Question

a cone of radius 10 cm is cut into two parts by a plane to the midpoint of its vertical Axis parallel to the base find the ratio of volume of its smaller cone and frustum of cone ​

Answer 1

Answer:

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