The volumes of two spheres are in the ratio of 64 : 27. The ratio of their surface areas is · ABC26GN5003
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: Bank P.O. 2010
The volumes of two spheres are in the ratio of 64 : 27. The ratio of their surface areas is
(a)1 : 2
(b)2 : 3
(c)9 : 16
(d)16 : 9
Answer
Answer (as printed): D
Explanation
Let their radii be $R$ and $r$. Then, $$\frac{\frac{4}{3} \pi R^{3}}{\frac{4}{3} \pi r^{3}}=\frac{64}{27} \Rightarrow\left(\frac{R}{r}\right)^{3}=\frac{64}{27}=\left(\frac{4}{3}\right)^{3} \Rightarrow \frac{R}{r}=\frac{4}{3} .$$
Explanation as extracted from the printed page; notation may be imperfect.