A solid cylinder of radius R and height frac R 2 is melted and recast into N identical solid spheres. If the total surface area of all spheres equals the total surface area of the original cylinder, what is N?

Home › MCQs › EEJ MAIN Aptitude › Question #10989

EEJ MAIN Aptitude QUESTION #10989

Question 1

A solid cylinder of radius $R$ and height $\frac{R}{2}$ is melted and recast into $N$ identical solid spheres. If the total surface area of all spheres equals the total surface area of the original cylinder, what is $N$?

$2$
$3$✔️
$4$
$6$

Correct Answer Explanation

Volume of cylinder: $V_c = \pi R^2 \cdot \frac{R}{2} = \frac{\pi R^3}{2}$. Volume of $N$ spheres: $N \cdot \frac{4}{3}\pi r^3 = \frac{\pi R^3}{2}$, so $Nr^3 = \frac{3R^3}{8}$. Surface area of cylinder: $SA_c = 2\pi R^2 + 2\pi R \cdot \frac{R}{2} = 3\pi R^2$. Surface area of $N$ spheres: $N \cdot 4\pi r^2 = 3\pi R^2$, so $Nr^2 = \frac{3R^2}{4}$. Dividing: $r = \frac{3R^3/8}{3R^2/4} = \frac{R}{2}$. Substituting: $N \cdot \frac{R^2}{4} = \frac{3R^2}{4}$, giving $N = 3$.

More Options