Hemisphere — Volume is 19404 cm^3. Find its total surface area (TSA).

Introduction / Context:
For a hemisphere, volume V = (2/3)πr^3 and total surface area (TSA) = 3πr^2 (curved area + base).

Given Data / Assumptions:

• V = 19404 cm^3
• Use π = 22/7 for exact integers

Concept / Approach:
Find r from volume, then compute TSA.

Step-by-Step Solution:
(2/3)πr^3 = 19404 ⇒ (44/21)r^3 = 19404 ⇒ r^3 = 19404 * 21 / 44 = 441 * 21 = 9261 = 21^3r = 21 cmTSA = 3πr^2 = 3 * (22/7) * 441 = 66 * 63 = 4158 sq. cm

Verification / Alternative check:
Back-substitute r into volume: (2/3)*(22/7)*9261 = 19404 ✔

Why Other Options Are Wrong:
27772 is far too large; 5544 and 1386 mismatch 3πr^2.

Common Pitfalls:
Using curved area 2πr^2 instead of TSA 3πr^2.

Final Answer:
4158 sq. cm