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EEJ MAIN Aptitude QUESTION #11049
Question 1
A solid metal sphere of radius $R$ is melted and recast into a cone of height $H = R$ and base radius $r$. What is $\frac{r}{R}$?
  • $\sqrt{2}$
  • $\sqrt{3}$
  • $2$✔️
  • $\frac{\sqrt{3}}{2}$
Correct Answer Explanation
Volume of sphere: $\frac{4}{3}\pi R^3$. Volume of cone: $\frac{1}{3}\pi r^2 H = \frac{1}{3}\pi r^2 R$. Equating: $\frac{4}{3}\pi R^3 = \frac{1}{3}\pi r^2 R$. Simplifying: $4R^2 = r^2$, so $r = 2R$. Thus $\frac{r}{R} = 2$.