CAT 2020 Exam Shift 1 Solved Paper

Question : 76 of 76

Marks: +1, -0

A solid right circular cone of height

27 {cm}

is cut into two pieces along a plane parallel to its base at a height of

18 {cm}

from the base. If the difference in volume of the two pieces is

225 {cc}

, the volume, in

{cc}

, of the original cone is

Validate

Solution:

As the cone is cut at one-third height from the top (the vertex), the total volume is proportional to the cubes of the heights of the two parts.
Ratio of volumes two parts

=(\;{1}/{3})^{3}: 1^{3}=1: 27

Hence the bottom part will have volume of

27-1

i.e., 26 parts.
Given

(26-1)

i.e., 25 parts

-225 {cc}

.
Hence the required answer is 27 parts

=\;{27 × 225}/{25}=243 {cc}

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