The diameter of a copper sphere is 6 cm. The sphere is melted and is drawn…

Concept

Melting a solid and redrawing it conserves volume. No copper is created or destroyed, so whatever new shape the metal takes, its volume is exactly the volume of the original sphere.

Two formulas carry this: a sphere of radius R has volume V = (4/3)πR3, and a wire of uniform circular cross-section is a right circular cylinder, so a wire of radius r and length h has volume V = πr2h.

Applying it here

1. The sphere's diameter is 6 cm, so its radius is R = 6 ÷ 2 = 3 cm.

2. Volume of the sphere = (4/3)πR3 = (4/3)π(3)3 = (4/3)π × 27 = 36π cm3.

3. The wire is a cylinder of length h = 36 cm and unknown radius r, so its volume = πr2h = πr2 × 36 = 36πr2 cm3.

4. Conservation of volume equates the two: 36πr2 = 36π.

5. Dividing both sides by 36π gives r2 = 1, and a radius is positive, so r = 1 cm.

Cross-check

Substitute back: a wire of radius 1 cm and length 36 cm holds π × 12 × 36 = 36π cm3, exactly the volume of the sphere, so r = 1 cm is right.

Result

The radius the question asks for is 1 cm. That value is not 0.5 cm, 1.5 cm or 2 cm, and because πr2 × 36 increases strictly with r, no two different radii could both satisfy the condition either. The response that fits is “None of the above”.