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 the metallic sphere, R = 6 cm

Height of the cylinder, h = 32 cm

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

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

Hence, radius of the cylinder is 3 cm.

(ii) Curved surface area of cylinder = 2πrh

= 2 × 3.1 × 3 × 32

= 595.2 cm²

Hence, curved surface area of the cylinder is 595.2 cm².