A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. Find the :

(i) radius of the cylinder

(ii) curved surface area of the cylinder. Take π = 3.1

(i) Radius of metallic sphere (R) = 6 cm

Height of cylinder (h) = 32 cm

Volume of cylinder = Volume of metallic sphere (As sphere is melted and formed into a cylinder).

Let radius of cylinder = r cm.

$\therefore πr^2h = \dfrac{4}{3}πR^3 \\[1em]\Rightarrow r^2 = \dfrac{4π \times 6^3}{3 \times π \times 32} \\[1em] \Rightarrow r^2 = \dfrac{4 \times 216}{96} \\[1em] \Rightarrow r^2 = \dfrac{864}{96} \\[1em] \Rightarrow r^2 = 9 \\[1em] \Rightarrow r = \sqrt{9} = 3 \text{ cm}.$

Hence, the radius of the cylinder = 3 cm.

(ii) Curved surface area of cylinder = 2πrh

Putting values we get,

Curved surface area of cylinder = 2 × 3.1 × 3 × 32 = 595.2 cm².

Hence, curved surface area of cylinder = 595.2 cm².