Question:
The radii of two cylinders are in the ratio 3 : 5. If their heights are in the ratio 2 : 3, then the ratio of their curved surface areas is
(a) 2 : 5
(b) 5 : 2
(c) 2 : 3
(d) 3 : 5
Solution:
Given that
$r_{1}: r_{2}=3: 5$ and $h_{1}: h_{2}=2: 3$
Then,
The ratio of C.S.A. of cylinders
$\frac{s_{1}}{s_{2}}=\frac{2 \pi r_{1} h_{1}}{2 \pi r_{2} h_{2}}$
$\frac{s_{1}}{s_{2}}=\left(\frac{r_{1}}{r_{2}}\right) \times\left(\frac{h_{1}}{h_{2}}\right)$
$=\frac{3}{5} \times \frac{2}{3}$
$\frac{s_{1}}{s_{2}}=\frac{2}{3}$
$s_{1}: s_{2}=2: 5$
Hence, the correct answer is choice (a).