Sphere where volume equals surface area (numerically): If a sphere’s volume equals its surface area numerically, find its radius (units consistent).

Introduction / Context:
Setting two formulas equal tests algebraic manipulation. For spheres: Volume V = (4/3)πr^3 and Surface area S = 4πr^2. Equating V and S “numerically” means the numbers match in the same unit system.

Given Data / Assumptions:

• V = (4/3)πr^3
• S = 4πr^2
• V = S (numerically)

Concept / Approach:
Divide both sides by 4πr^2 (positive for r > 0) to isolate r.

Step-by-Step Solution:
(4/3)πr^3 = 4πr^2Divide by 4πr^2 → r/3 = 1r = 3 (units)

Verification / Alternative check:
Compute both sides at r = 3: V = (4/3)π * 27 = 36π; S = 4π * 9 = 36π. Equal indeed.

Why Other Options Are Wrong:
1, 2, and 4 do not satisfy r/3 = 1; 6 makes V triple S. Only 3 works.

Common Pitfalls:
Dropping π incorrectly; treating equality as dimensional rather than numerical; accepting r = 0 (invalid radius).

Final Answer:
3 unit