Q6 of 79 Page 244

The radius of a solid sphere is 24 cm. It is melted and drawn into a long wire of uniform cross section. Find the length of the wire if its radius is 1.2 mm.

Given, Radius of a solid sphere(r) = 24 cm


Radius of wire (R) = 1.2 mm = 0.12 cm


length of the wire(l) = ?


Solid sphere is melted and drawn into a long wire of uniform cross section. Thus,


Volume of sphere = Volume of wire(cylinder)


⇒ r3 = r2l


⇒ (24)3 = (0.12)2l


⇒ (24)3 = (0.12)2l


⇒ l =


⇒ l =


⇒ l = 128100100


⇒ l = 12.8 km


The length of the wire is 12.8 km.


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