The area of the curved surface of a cylinder is 4400 cm², and the circumference of its base is 110 cm. Find :

(i) the height of the cylinder.

(ii) the volume of the cylinder.

(i) Given, curved surface area of cylinder = 4400 cm².

We know that curved surface area of cylinder = 2πrh.

∴ 2πrh = 4400 …..(i)

Given, circumference of base = 110 cm.

We know that circumference = 2πr.

∴ 2πr = 110 …..(ii)

Dividing equation (i) by (ii),

$\Rightarrow \dfrac{2πrh}{2πr} = \dfrac{4400}{110}$

⇒ h = 40 cm.

Hence, the height of the cylinder = 40 cm.

(ii) We know that circumference = 2πr.

Given, circumference = 110 cm.

∴ 2πr = 110

⇒ $2 \times \dfrac{22}{7}r$ = 110

⇒ r = $\dfrac{110 \times 7}{2 \times 22} = \dfrac{770}{44}$ = 17.5 cm.

Volume of cylinder = πr²h.

Putting values we get,

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

Hence, the volume of the cylinder = 38500 cm³.