# 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.

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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