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SSC CPO 2025 PYQ — Question 107

SSC CPO - 9 Dec 2025 - Shift 1 • Quantitative Aptitude • Q107

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A right circular cone is cut into two parts of equal height by a horizontal plane. What is the ratio of the volumes of the smaller cone to the frustum?

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Correct answer: B

Explanation

The cone is cut at an equal height ⇒ Height of the smaller cone = H/2
Ratio of radii = Ratio of heights ⇒ r/R = 1/2
Volume of the smaller cone =r2h⇒(12)2×(12)=18= r^2 h \Rightarrow \left(\frac{1}{2}\right)^2 \times \left(\frac{1}{2}\right) = \frac{1}{8}
That is, the smaller cone = 1/8 (of the full cone)
Volume of the Frustum =1−18=78= 1 - \frac{1}{8} = \frac{7}{8}
Smaller cone : Frustum =18:78=1:7= \frac{1}{8} : \frac{7}{8} = 1 : 7