Question

The ratio of radii of two cylinders is $1:\sqrt{3}$ and their heights are in the ratio 2 : 3. The ratio of their curved surface area is:

• A. $4:3\sqrt{3}$
• B. $2:3\sqrt{3}$
• C. $3:2\sqrt{3}$
• D. $1:\sqrt{3}$

Answer 1

The correct option is B $2:3\sqrt{3}$

Let the radii be $r$ and $\sqrt{3}r$ and heights be $2h$ and $3h$ respectively.

The curved surface area of a cylinder is given by $2\pi \left(radius\right)\left(height\right)$.

Ratio of their curved surface area

$=2\pi r\left(2h\right):2\pi \left(\sqrt{3}r\right)\left(3h\right)$

$=\frac{2\pi r\times 2h}{2\pi \sqrt{3}r\times 3h}$

$=\frac{2}{3\sqrt{3}}$

Therefore, the required ratio is $2:3\sqrt{3}$.