Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
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.