If a cone is divided into two parts by drawing a plane through the midpoints of its axis then the ra...........

Quantitative Aptitude (CGL) Mensuration 3D

If a cone is divided into two parts by drawing a plane through the midpoints of its axis, then the ratio of the volume of the 2 parts of the cone is

1 : 2

1 : 4

1 : 7

1 : 8

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Explanation:

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) = (1/3)πr^2h
Volume of the cone (A,B,C)
= (1/3)πr^2.(2r)^2(2h)
= (8/3)πr^2h
Volume of the portion (PB, OC) = Volume of the cone (A, BC) - Volume of the cone (A, PQ)
= (8/3)πr^2h - (1/3)πr^2h
= (7/3)πr^2h
Required ratio = ((1/3)πr^2h)/((7/3)πr^2h)
= 1/ 7 = 1 : 7