The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. Find the

(i) radius of the cylinder.

(ii) volume of the cylinder.

(i) Circumference = 2πr.

Given, circumference = 132 cm.

∴ 2πr = 132

⇒ $2 \times \dfrac{22}{7}r$ = 132

⇒ r = $\dfrac{132 \times 7}{2 \times 22} = \dfrac{924}{44}$ = 21 cm.

Hence, the radius of the cylinder = 21 cm.

(ii) Given height = 25 cm.

Volume of cylinder = πr²h.

Putting values we get,

$\text{Volume of cylinder } = \dfrac{22}{7} \times (21)^2 \times 25 \\[1em] = \dfrac{22 \times 441 \times 25}{7} \\[1em] = \dfrac{242550}{7} \\[1em] = 34650 \text{ cm}^3.$

Hence, the volume of the cylinder = 34650 cm³.