A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, find its width.

Let the diameter of sphere be ‘D’ and Radius of sphere be ‘R’


∴ D = 8 m


Also, we know


R = D/2


⇒ R = 8/2


∴ R = 4 m


Explanation: Here the volume of sphere will be equal to the volume of the resulting cylinder as the resulting cylinder is formed by melting the sphere.


Volume of the sphere, V1





Let the length/height of the cylinder be ‘H’ and let the radius of the cylinder be ‘r’ and volume of the cylinder be ‘V2’


∴ H = 12 m


Volume of the cylinder = V2 = π(r2)H


⇒ V2 = π(r2) × 12 (putting value of H)


⇒ V2 = 12π × r2 m3→eqn2


Now equate equation 1 and 2,


⇒ V2 = V1








∴ r = 2.66 m


Width of cylinder = diameter of cylinder = 2 × radius


⇒ Width of cylinder = 2 × r


⇒ Width of cylinder = 2 × 2.66


∴ Width of cylinder = 5.32 m


Width of the resulting cylinder is 5.32 m


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