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

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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