Q14 of 67 Page 195

The diameter of a metallic sphere is 6 cm. It is melted section. If the length of the wire is 36 m, then find the radius of the wire.

Diameter of sphere = 6 cm


Radius of sphere = rs = = 3 cm


Length of wire = h = 36 m = 3600 cm


Let the radius of wire be rw


Wire is cylindrical


Wire is formed by melting the sphere thus volume of wire is same as volume of sphere


Volume of sphere = πrs3


Volume of cylindrical wire = πrw2h


⇒ πrs3 = πrw2h


⇒ × rs3 = rw2 × h


Substitute values


⇒ × 33 = rw2 × 3600


⇒ 4 × 32 = rw2 × 3600


⇒ 36 = rw2 × 3600


⇒ rw2 =


⇒ rw = 0.1 cm


Therefore, radius of wire is 0.1 cm


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