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