Q. 85.0( 2 Votes )

The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of the wire.

Answer :

Given: diameter of sphere = 42 cm


radius of sphere = 42/2 = rs = 21 cm


Diameter of cylindrical wire = 2.8 cm


Radius of cylindrical wire = rc = 1.4 = (7/5)cm


Let l be the length of wire


Formula: volume of sphere = (4/3)πrs3


Volume of wire = πrc2l


Sphere is melted and wire is made from it


volume of sphere = volume of wire


(4/3)πrs3 = πrc2l


4 × 213 = 3 × (7/5)2 × l


4 × 21 × 9 × 25 = 3 × l


2100 × 3 = l


l = 6300 cm


Therefore length of wire formed = 6300 cm = 63 meters


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