Question

The radii of two right circular cylinders are in the ratio 2:3 and their heights are in the ratio 5:4. Calculate the ratio of their curved surface areas.

• A. 7 : 8
• B. 5 : 9
• C. 5 : 6
• D. 3 : 8

Answer 1

The correct option is C 5 : 6


Let the radii of two cylinders be $2r$ and $3r$, their heights be $5h$ and $4h$ respectively.
Curved surface area of 1st cylinder = $2\times \pi \times 2r\times 5h$
Curved surface area of 2nd cylinder $C_2=2\times \pi \times 3r\times 4h$

$\frac{C_1}{C_2}=\frac{2\times \pi \times 2r\times 5h}{2\times \pi \times 3r\times 4h}=\frac{5}{6}$

Required ratio is 5:6
Hence, the correct answer is option (c)