A solid metallic sphere of 2 cm radius is melted and converted to a cube. The side of the cube is approximately equal to :

When a solid object is melted and reshaped, its volume remains constant. The volume of a sphere is calculated using the formula V = ⁴⁄₃πr³. Given the radius (r) is 2 cm, the volume is:

V = ⁴⁄₃ × π × (2)³ = ⁴⁄₃ × π × 8 = ^32π⁄₃

Using the approximate value of π ≈ 3.14159:
V ≈ ^{32 × 3.14159}⁄₃ ≈ ^100.53⁄₃ ≈ 33.51 cm³

The volume of a cube with side 'a' is V = a³. Setting the volumes equal:
a³ ≈ 33.51
a = ³√33.51

Testing the options:
3.2³ = 32.768
3.3³ = 35.937
Since 33.51 is closest to 32.768, the side of the cube is approximately 3.2 cm.