CAT 2020 Slot 1 QA Q17 Mensuration

Question 17 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to it's base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, the volume, in cc, of the original cone is
  1. A
    264
  2. B
    232
  3. C
    243
  4. D
    256

Answer: (C) 243 Mensuration MCQ

Solution

  1. The cut at height 18 leaves a top cone of height 9 = \(\frac13\) of 27, so its volume is \(\frac{V}{27}\).
  2. Frustum \(= \frac{26V}{27}\). Difference \(= \frac{25V}{27} = 225 \Rightarrow V = 243\).

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