Curved surface area from given sphere volume: A sphere has volume V = (88/21) × 14^3 cm^3. Find its curved surface area (cm^2).

Introduction / Context:Recognize that (4/3)π matches (88/21) when π is taken as 22/7, a standard competition convention. This makes solving for r immediate, then CSA = 4πr^2 follows.

Given Data / Assumptions:

• V = (88/21) * 14^3 cm^3
• Sphere formulas: V = (4/3)πr^3; CSA = 4πr^2

Concept / Approach:Note (4/3)π = (4/3)*(22/7) = 88/21. Therefore, (88/21)r^3 = (88/21)*14^3 ⇒ r = 14 cm. Then compute CSA.

Step-by-Step Solution:r = 14 cmCSA = 4πr^2 = 4π * 196 = 784πWith π = 22/7 → 784 * 22/7 = 112 * 22 = 2464 cm^2

Verification / Alternative check:Back-substitute r into V: (4/3)π * 14^3 = (88/21)*14^3, consistent with the given V.

Why Other Options Are Wrong:Values 2424, 2446, 2484 deviate from exact 2464 with π = 22/7; 2400 is a rounded guess, not exact.

Common Pitfalls:Trying to compute π more precisely breaks the designed integer match; mixing diameter and radius when squaring.

Final Answer:2464 cm^2