Melting a solid sphere (radius 9 cm) into a thin wire (radius 1 mm):\nFind the length of the wire (in metres). Take π = 22/7.

Introduction / Context:
Volume is conserved during melting and reshaping. Equate the sphere’s volume to the cylinder (wire) volume and solve for the wire length. Unit consistency is essential (mm vs cm).

Given Data / Assumptions:

• Sphere radius R = 9 cm.
• Wire radius r = 1 mm = 0.1 cm.
• π = 22/7.

Concept / Approach:
Sphere volume V_s = (4/3)πR^3. Wire (cylinder) volume V_c = πr^2L. Set V_s = V_c and solve L.

Step-by-Step Solution:

Verification / Alternative check:
Cancel π on both sides; convert cm to m at the end (divide by 100).

Why Other Options Are Wrong:
1166.4 m, 1458 m, 777.6 m, 648 m arise from arithmetic or unit-conversion errors; 972 m matches exact conservation.

Common Pitfalls:
Forgetting to convert 1 mm to cm (0.1 cm), or neglecting to square the wire radius.

Final Answer:
972 metres