Wire length from melted sphere: A solid copper sphere of diameter 18 cm is melted and drawn into a wire of radius 0.2 mm. Find the length of the wire (in meters).

Introduction / Context:Volume is conserved when a solid is melted and redrawn. Compute the sphere’s volume and equate it to the cylindrical wire’s volume to solve for the wire length. Unit consistency (mm to cm) is crucial.

Given Data / Assumptions:

• Sphere diameter = 18 cm ⇒ radius r_s = 9 cm
• Wire radius r_w = 0.2 mm = 0.02 cm
• V_sphere = (4/3) π r_s^3; V_wire = π r_w^2 * L

Concept / Approach:

• Set V_sphere = V_wire and solve for L.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 243 m / 2430 m / 24.3 m: Off by powers of 10 due to unit conversion or squaring radius mistakes.

Common Pitfalls:

• Using radius 0.2 cm instead of 0.2 mm = 0.02 cm.
• Forgetting to square the wire radius in π r^2 L.

Final Answer:

24300 m