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If a cone is divided in two parts by drawing a plane through mid - point of its axis, then ratio of the volumes of the 2 parts of the cone is

A) 1 : 2
B) 1 : 4
C) 1 : 7
D) 1 : 8

Correct Answer:



C) 1 : 7

Description for Correct answer:

Let PQ be the plane which passes through middle point O of the axis AO of the cont(A,BC).

Let r be the radius of the cone (A, PQ) and h its height. Then, from geometry, radius of the cone (A,BC) is 2r and its height is 2h.

Volume of the cone (A, PQ) = \( \Large\frac{1}{3} \pi r^2 h \)

Volume of the cone (A,B,C)

= \( \Large\frac{1}{3} \pi r^2.(2r)^2(2h)\)

= \( \Large\frac{8}{3} \pi r^2 h\)

Volume of the portion (PB, OC) = Volume of the cone (A, BC) - Volume of the cone (A, PQ)

= \( \Large\frac{8}{3} \pi r^2 h\) - \( \large\frac{1}{3} \pi r^2 h\)

= \( \Large\frac{7}{3} \pi r^2 h\)

Required ratio = \( \Large\frac{ \Large\frac{1}{3} \pi r^2 h }{\large\frac{7}{3} \pi r^2 h} \)
= 1/ 7 = 1 : 7

Part of solved Ratio and Proportions questions and answers : >> Aptitude >> Ratio and Proportions

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