A cone has height h and radius r. The cone is melted and recast into a smaller cone whose height is h/2 and radius is r/3 . What fraction of the original volume is unused?

A cone has height h and radius r. The cone is melted and…

A cone has height h and radius r. The cone is melted and recast into a smaller cone whose height is $\frac{h}{2}$ and radius is $\frac{r}{3}$ . What fraction of the original volume is unused?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. $\frac{17}{18}$ .

Volume of original cone = (1/3)πr²h

Volume of smaller cone = (1/3)π(r/3)²(h/2) = (1/3)π(r²/9)(h/2) = (1/54)πr²h

Fraction used $= \frac{\frac{1}{54}\pi r^2h}{\frac{1}{3}\pi r^2h}$ = (1/54) × 3 = 1/18

Fraction unused = 1 – 1/18 = 17/18

SSC CGL 2025 PYQ — Question 63