The curved surface area of a cylinder is 4400 cm² and the circumference of its base is 110 cm. The volume of the cylinder (in cm³) is :

1. 36000

2. 38500

3. 40150

4. 42250

Given, curved surface area of cylinder = 4400 cm²

We know that curved surface area of cylinder = 2πrh

∴ 2πrh = 4400 …..(1)

Given, circumference of base = 110 cm

We know that circumference = 2πr

∴ 2πr = 110 …..(2)

$\Rightarrow 2 \times \dfrac{22}{7} \times \text{r} = 110 \\[1em] \Rightarrow \text{r} = \dfrac{110 \times 7}{22 \times 2} \\[1em] \Rightarrow \text{r} = \dfrac{770}{44} \\[1em] \Rightarrow \text{r} = 17.5 \text{ cm.}$

Dividing eq.(1) by (2), we get:

$\dfrac{2π\text{rh}}{2π\text{r}} = \dfrac{4400}{110}$

⇒ h = 40 cm

Volume of cylinder = πr²h

$= \dfrac{22}{7} \times 17.5^2 \times 40 \\[1em] = \dfrac{22}{7} \times 306.25 \times 40 \\[1em] = \dfrac{269500}{7} \\[1em] = 38500 \text{ cm}^3.$

Hence, option 2 is the correct option.