Sphere with given surface area — compute volume exactly: If a sphere has surface area 616 sq cm, find its volume (in cubic centimeters).

Introduction / Context:
Given a sphere’s surface area, solve for its radius and then compute the volume. The numbers are chosen so that using π = 22/7 leads to exact integer simplification.

Given Data / Assumptions:

• S = 4πr^2 = 616 cm2.
• π = 22/7 (standard in such aptitude items).
• Volume V = (4/3)πr^3.

Concept / Approach:
From 4πr^2 = 616, obtain r first. Then substitute into V = (4/3)πr^3 and simplify exactly.

Step-by-Step Solution:
r^2 = 616/(4π) = 154/π = 154 * 7/22 = 49 ⇒ r = 7 cmV = (4/3)πr^3 = (4/3)π * 343 = (1372/3)πWith π = 22/7: V = (1372/3) * (22/7) = (196 * 22)/3 = 4312/3 cm3

Verification / Alternative check:
Decimal check: 4312/3 ≈ 1437.33 cm3, reasonable for r = 7 cm.

Why Other Options Are Wrong:
Other fractions do not match the exact cancellation with r = 7 and π = 22/7.

Common Pitfalls:
Using 616/π as if it were 616/3.14 with premature rounding; mis-evaluating r from S.

Final Answer:
4312/3 cm3