If a solid circular cylinder of iron whose diameter is 15 cm and height 10 cm is melted and recasted into a sphere, then the radius of the sphere is

1. 15 cm

2. 10 cm

3. 7.5 cm

4. 5 cm

Diameter of cylinder = 15 cm

For cylinder,

Radius (r) = $\dfrac{15}{2} = 7.5$ cm and height (h) = 10 cm.

Let radius of sphere be R.

Volume of cylinder = Volume of sphere.

$\Rightarrow πr^2h = \dfrac{4}{3}πR^3 \\[1em] \Rightarrow r^2h = \dfrac{4}{3}R^3 \\[1em] \Rightarrow R^3 = \dfrac{3 \times (7.5)^2 \times 10}{4} \\[1em] \Rightarrow R^3 = \dfrac{1687.5}{4} \\[1em] \Rightarrow R^3 = 421.875 \\[1em] \Rightarrow R^3 = (7.5)^3 \\[1em] \Rightarrow R = 7.5 \text{ cm}.$

Hence, Option 3 is the correct option.