Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2016 · Marks: · Difficulty:
A sphere and a cube have same surface area. The ratio of squares of their volumes is
(a)$6: \pi$
(b)$5: \pi$
(c)3 : 5
(d)1 : 1
Answer
Answer (as printed): A
Explanation
Let the radius of the sphere be R and length of each side of the cube $=a$ Surface area of sphere $=4 \pi \mathrm{R}^{2}$ Surface area of a cube $=6 a^{2}$ $$\begin{aligned} & \Rightarrow 4 \pi r^{2}=6 a^{2} \\ & \Rightarrow \frac{R^{2}}{a^{2}}=\frac{6}{4 \pi}=\frac{3}{2 \pi} \end{aligned}$$ Radio of the square of the volumes $$=\frac{\left(\frac{4}{3} \pi R^{3}\right)^{2}}{\left(a^{3}\right)^{2}}$$ $\Rightarrow \frac{16 \pi^{2}}{9}\left(\frac{R^{2}}{a^{2}}\right)^{3}$ $$=\frac{16}{9} \pi^{2} \cdot\left(\frac{3}{2 \pi}\right)^{3}$$
Explanation as extracted from the printed page; notation may be imperfect.