The capacities of two hemispherical vessels are 6.4 litres and 21.6 litres. The areas of inner curved… · ABC26GN5044
Subject: General Aptitude · Chapter: Volume and Surface Area
The capacities of two hemispherical vessels are 6.4 litres and 21.6 litres. The areas of inner curved surfaces of the vessels will be in the ratio of
(a)$\sqrt{2}: \sqrt{3}$
(b)2 : 3
(c)4 : 9
(d)16 : 81
Answer
Answer (as printed): C
Explanation
Let their radii be $R$ and $r$. Then, $$\frac{\frac{2}{3} \pi R^{3}}{\frac{2}{3} \pi r^{3}}=\frac{6.4}{21.6} \Leftrightarrow\left(\frac{R}{r}\right)^{3}=\frac{8}{27}=\left(\frac{2}{3}\right)^{3} \Leftrightarrow \frac{R}{r}=\frac{2}{3} .$$ ∴ Ratio of curved surface areas $=\frac{2 \pi R^{2}}{2 \pi r^{2}}=\left(\frac{R}{r}\right)^{2}=\frac{4}{9}$.
Explanation as extracted from the printed page; notation may be imperfect.