If two cylinders of equal volumes have their heights in the ratio 2 : 3, then the ratio of their radii is · ABC26GN4908
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: Bank P.O. 2010
If two cylinders of equal volumes have their heights in the ratio 2 : 3, then the ratio of their radii is
(a)$\sqrt{6}: \sqrt{3}$
(b)$\sqrt{5}: \sqrt{3}$
(c)2 : 3
(d)$\sqrt{3}: \sqrt{2}$
Answer
Answer (as printed): D
Explanation
Let their heights be $2 h$ and $3 h$ and radii be $r$ and $R$ respectively. Then, $$\pi r^{2}(2 h)=\pi R^{2}(3 h) \Rightarrow \frac{r^{2}}{R^{2}}=\frac{3}{2} \Rightarrow \frac{r}{R}=\frac{\sqrt{3}}{\sqrt{2}} \text { i.e. } \sqrt{3}: \sqrt{2} .$$
Explanation as extracted from the printed page; notation may be imperfect.