If a solid right circular cone of height 24 cm and base radius 6 cm is melted and recast in the shape of sphere, then the radius of the sphere is

1. 4 cm

2. 6 cm

3. 8 cm

4. 12 cm

Since, cone is recasted into sphere.

∴ Volume of cone = Volume of sphere.

Given, radius of cone (R) = 6 cm, height (h) = 24 cm.

Let the radius of sphere be r.

$\therefore \dfrac{1}{3}πR^2h = \dfrac{4}{3}πr^3$

Multiplying both sides by 3 and dividing by π we get,

$\Rightarrow R^2h = 4r^3 \\[1em] \Rightarrow 6^2 \times 24 = 4r^3 \\[1em] \Rightarrow 4r^3 = 36 \times 24 \\[1em] \Rightarrow r^3 = \dfrac{864}{4} \\[1em] \Rightarrow r^3 = 216 \\[1em] \Rightarrow r^3 = (6)^3 \\[1em] \Rightarrow r = 6 \text{ cm}.$

Hence, Option 2 is the correct option.