SarkariPYQ

SSC CPO 2025 PYQ — Question 111

SSC CPO - 9 Dec 2025 - Shift 2 • Quantitative Aptitude • Q111

Back to paper

A cone is melted down and recast into smaller cones, each having a radius and height equal to one-third of the original cone. How many such small cones can be formed in total?

Show answer & explanation

Correct answer: A

Explanation

Radius of the small cone = (1/3)R

Height of the small cone = (1/3)H

Volume =13πr2h= \frac{1}{3}\pi r^2 h

Original Volume =13πR2H= \frac{1}{3}\pi R^2 H

Volume of the small cone =13π(R3)2(H3)=181πR2H= \frac{1}{3}\pi \left(\frac{R}{3}\right)^2 \left(\frac{H}{3}\right) = \frac{1}{81}\pi R^2 H

Number = (Original Volume)/(Volume of the small cone) =13πR2H181πR2H=27= \frac{\frac{1}{3}\pi R^2 H}{\frac{1}{81}\pi R^2 H} = 27