Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2009 · Marks: · Difficulty:
If the surface areas of two spheres are in the ratio of $4: 25$, then the ratio of their volumes is
(a)4 : 25
(b)25 : 4
(c)125 : 8
(d)8 : 125
Answer
Answer (as printed): D
Explanation
Let their radii be $R$ and $r$. Then, $\frac{4 \pi R^{2}}{4 \pi r^{2}}=\frac{4}{25} \Rightarrow\left(\frac{R}{r}\right)^{2}=\left(\frac{2}{5}\right)^{2} \Rightarrow \frac{R}{r}=\frac{2}{5}$. ∴ Ratio of volumes $=\frac{\frac{4}{3} \pi R^{3}}{\frac{4}{3} \pi r^{3}}=\left(\frac{R}{r}\right)^{3}=\left(\frac{2}{5}\right)^{3}=\frac{8}{125}$.
Explanation as extracted from the printed page; notation may be imperfect.