CAT 2020 Quant Question [Slot 1] with Solution 26

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.