A solid piece of iron in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm is molded to form a sphere. The radius of the sphere is

1. 21 cm

2. 23 cm

3. 25 cm

4. 19 cm

Since, the cuboid is molded into a sphere.

Let radius of sphere be r cm.

∴ Volume of cuboid = Volume of sphere.

$\therefore 49 \times 33 \times 24 = \dfrac{4}{3}πr^3 \\[1em] \Rightarrow r^3 = \dfrac{49 \times 33 \times 24 \times 3}{4 \times \dfrac{22}{7}} \\[1em] \Rightarrow r^3 = \dfrac{49 \times 33 \times 24 \times 3 \times 7}{4 \times 22} \\[1em] \Rightarrow r^3 = \dfrac{814968}{88} \\[1em] \Rightarrow r^3 = 9261 \\[1em] \Rightarrow r^3 = (21)^3 \\[1em] \Rightarrow r = 21 \text{ cm}.$

Hence, Option 1 is the correct option.