Correct Answer - Option 1 : 2016 m
Given:
Radius of cylindrical wire = 7mm
Radius of copper sphere = 42 cm
Formula used:
Volume of cylindrical wire = πr2h
Volume of copper sphere = 4/3 × πR3
Calculation:
Radius of cylindrical wire = 7mm = (7/10) cm
Radius of copper sphere = 42 cm
Suppose the length of the cylindrical wire is x.
Volume of cylindrical wire = πr2h = π(7/10)2 × x
Volume of copper sphere = 4/3 × πR3 = (4/3) × 423
According to question –
∴ π(7/10)2 × x = (4/3) × 423
⇒ (7 × 7 × x)/100 = 4/3 × (42 × 42 × 42)
⇒ x/100 = 4/3 × 6 × 6 × 42
⇒ x/100 = 2016
⇒ x = 201600 cm
⇒ x = 201600/100 m
⇒ x = 2016 m
∴ The length of the cylindrical wire is 2016 meter.
