Cone — Vertical height 24 cm and volume 1232 cm^3. Find the curved surface area (CSA).

Introduction / Context:
Given cone volume and height, find radius, then slant height and CSA. Use V = (1/3)πr^2h, l = √(r^2 + h^2), CSA = π r l.

Given Data / Assumptions:

• h = 24 cm
• V = 1232 cm^3
• Use π = 22/7 for neat integers

Concept / Approach:
Compute r from 8πr^2 = 1232 (since (1/3)*24 = 8), then l, then CSA.

Step-by-Step Solution:
8πr^2 = 1232 ⇒ r^2 = 154/π = 49 (with π = 22/7) ⇒ r = 7 cml = √(r^2 + h^2) = √(49 + 576) = √625 = 25 cmCSA = π r l = (22/7) * 7 * 25 = 550 cm2

Verification / Alternative check:
Volume back-check: (1/3)*π*7^2*24 = 1232 cm^3 ✔

Why Other Options Are Wrong:
704, 616, 1254, and 154 cm2 result from arithmetic or formula mix-ups.

Common Pitfalls:
Using height instead of slant height in CSA.

Final Answer:
550 cm2