ABC26GN5015 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2006 · Marks: · Difficulty:
A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of the cube is
(a)$\sqrt{\pi}: \sqrt{6}$
(b)$\sqrt{2}: \sqrt{\pi}$
(c)$\sqrt{\pi}: \sqrt{3}$
(d)$\sqrt{6}: \sqrt{\pi}$
Answer
Explanation
$4 \pi R^{2}=6 a^{2} \Rightarrow \frac{R^{2}}{a^{2}}=\frac{3}{2 \pi} \Rightarrow \frac{R}{a}=\frac{\sqrt{3}}{\sqrt{2 \pi}}$. $$\begin{aligned} \frac{\text { Volume of sphere }}{\text { Volume of cube }}=\frac{\frac{4}{3} \pi R^{3}}{a^{3}}=\frac{4}{3} \pi \cdot\left(\frac{R}{a}\right)^{3} & =\frac{4}{3} \pi \cdot \frac{3 \sqrt{3}}{2 \pi \sqrt{2 \pi}} \\ & =\frac{2 \sqrt{3}}{\sqrt{2 \pi}}=\frac{\sqrt{12}}{\sqrt{2 \pi}}=\frac{\sqrt{6}}{\sqrt{\pi}} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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