CAT 2020 Quant Question [Slot 1] with Solution 26

Question

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

  1. 232
  2. 256
  3. 264
  4. 243
Option: 4
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 \( = {\left( {\frac{1}{3}} \right)^3}:{1^3} = 1:27\)

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 \( = \frac{{27 \times 225}}{{25}}\) =243 cc.

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