The diameter of a metallic sphere is $6$ cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is $36$ m, find the radius of its cross-section.

Because the sphere is melted and drawn into a wire, the volume of the sphere equals the volume of the cylindrical wire. Using the formulas, (4/3) * pi * R^3 = pi * r^2 * L, where the sphere's radius R is 3 cm, the wire's length L is 3600 cm and r is the wire's radius. Substituting these values gives (4/3) * pi * 3^3 = pi * r^2 * 3600, which simplifies to 36 = r^2 * 3600, so r^2 = 0.01 and r = 0.1 cm. The radius of the cross-section is 0.1 cm.

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