Correct Answer - Option 3 : 1944 metre
Given:
Diameter of sphere = 36 cm
Diameter of wire = 4 mm
Formula used:
Volume of sphere = 4/3πR3
Volume of wire (cylinder) = πr2h
Where, R = Radius of sphere
r = radius of wire
Calculation:
Let the length of wire be h metre
Radius of sphere = 36/2 = 18 cm
Radius of wire = 4/2 = 2/10 mm = 0.2 cm
According to the question:
Volume of sphere = Volume of wire (cylinder)
⇒ 4/3πR3 = πr2h
⇒ (4/3) × (18)3 = (0.2)2h
⇒ (4/3) × (18 × 18 × 18) = (2/10) × (2/10) × h
⇒ R = 194400 cm = 194400/100 = 1944 metre
∴ The length of wire is 1944 metre.
