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