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A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. What is the ratio of the volumes of two parts?

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7:1

8:2

9:3

1:8

answer is A.

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Detailed Solution

It is given that a cone of radius 8cm and height 12cm is divided into two parts.
The radius of the cone after dividing into two parts:
As the cone is divided into two points through the midpoint, height is

h 2

. So,

r 1 r 2 = h 1 h r 1 8 = h 2 h r 1 = 4

The ratio of the volume of a frustum and volume of the cone:
Let the volume of the frustum be

V 1

, and volume of the cone be

V 2

. So,

V 1 V 2 = 13 π h 2 r 1 2 + r 2 2 + r 1 r 2 13 π r 1 2 h 1 V 1 V 2 = 6 42 + 82 + 4 ⋅ 8 42 ⋅ 6

V 1 V 2 = 71

The ratio of the volume of frustum and volume of smaller cones is 7:1.
Therefore, 1 is the correct option.

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