Recasting spheres — A lead sphere of radius 10 cm is melted into small spheres of radius 5 mm. How many small spheres are formed?

Introduction / Context:
Number formed equals ratio of volumes. For spheres, V ∝ r^3; π cancels in the ratio.

Given Data / Assumptions:

• Big radius R = 10 cm
• Small radius r = 0.5 cm (since 5 mm = 0.5 cm)

Concept / Approach:
N = (R^3) / (r^3) = (10^3) / (0.5^3).

Step-by-Step Solution:
N = 1000 / 0.125 = 8000

Verification / Alternative check:
Scaling by factor 20 in radius would give 20^3 = 8000 if r had been 0.5 vs 10 (factor 20).

Why Other Options Are Wrong:
800 and 400 are off by factors of 10 or 20; 125 is 5^3, unrelated.

Common Pitfalls:
Using diameter instead of radius; forgetting units (mm vs cm).

Final Answer:
8000