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SSC CGL 2025 PYQ — Question 63

SSC CGL - 18 Sep 2025 - Shift 2 • Quantitative Aptitude • Q63

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A cone is sliced into two sections by a plane that is parallel to its base, with the upper section representing 181\over8 of the overall volume. What is the ratio of the heights of the smaller cone to the original cone?

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 1 : 2.

For similar cones, volume ratio = (height ratio)3

Let original cone height = H and smaller cone height = h

Volume of smaller cone/Volume of original cone =(hH)3=18= \left( \frac{h}{H} \right)^3 = \frac{1}{8}

⇒ hH=183=12\frac{h}{H} = \sqrt[3]{\frac{1}{8}} = \frac{1}{2}

Required ratio = 1 : 2