A copper sphere of diameter 12 cm is drawn into a wire of diameter 4 mm. What is the length (in cm) of the wire?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 7200.
The diameter of a sphere = 12 cm
⇒ Radius of the sphere = Diameter/2 = 12/2 = 6 cm
Diameter of the wire = 4 mm = 0.4 cm
⇒ Radius of the wire = 0.4/2 = 0.2 cm
Let the length of the wire be x.
According to the question -
The volume of the copper wire = Volume of the copper sphere
⇒ πr2x = (4πR3)/3
⇒ x = (4R3)/(3r2) = (4 × 6 × 6 × 6)/(3 × 0.2 × 0.2) = 7200 cm