Cone — Base area = 154 cm2 and height = 14 cm. Find the curved surface area (CSA).

Introduction / Context:
We are given base area and height. From base area A_b = πr^2, find r, then slant height l = √(r^2 + h^2), and finally CSA = π r l.

Given Data / Assumptions:

• A_b = 154 cm2 = π r^2
• h = 14 cm
• Use π = 22/7

Concept / Approach:
Compute r from r^2 = 154 / π, then l, then CSA symbolically for an exact surd answer.

Step-by-Step Solution:
r^2 = 154 / (22/7) = 49 ⇒ r = 7 cml = √(r^2 + h^2) = √(49 + 196) = √245 = 7√5CSA = π r l = (22/7) * 7 * 7√5 = 154√5 cm2

Verification / Alternative check:
Dimensional check: area units cm2.

Why Other Options Are Wrong:
154√2 cm2 uses wrong sum under root; 11 and 5324 cm2 are invalid magnitudes; 308 cm2 would be π r h or misapplied formula.

Common Pitfalls:
Using height in place of slant height in CSA; not extracting r correctly from base area.

Final Answer:
154√5 cm2