The radius of a sphere is 6 cm. The sphere is melted and drawn into a wire of radius 0.4 cm .The length of the wire is :

Explanation

Given: Radius of the sphere = 6 cm Radius of the wire = 0.4 cm Concept used: Volume of cylinder = πr 2h Volume of sphere= (4/3)πr 3 Here, r = radius h = length Calculation: Radius of sphere R = 6 cm Radius of wire r = 0.2 cm and Let the length of wire be h cm Volume of wire = volume of sphere As we know, Volume of cylinder = πr2h Volume of sphere = (4/3) πr3 Let the length of the wire be h According to the question, Volume of cylinder = Volume of sphere So, π × (0.4) 2× h = (4/3) × π × 6 3 ⇒ 0.4 × 0.4 × h = (4/3) × 6 × 6 × 6 ⇒ h = 288/.16 ⇒ h = 1800 cm or 18 m [As 1 m = 100 cm] ∴ The length of the wire is 18 m.