Right circular cone – find slant height from curved surface area: A cone has radius 14 cm and curved surface area 440 cm^2. Compute its slant height l (in cm).

Introduction / Context:The curved (lateral) surface area of a right circular cone equals πrl, where r is the base radius and l is the slant height. This item checks rearrangement of the CSA formula to isolate l.

Given Data / Assumptions:

• CSA = 440 cm^2
• r = 14 cm
• Use π = 22/7 (yields an exact result here)
• CSA formula: πrl

Concept / Approach:From πrl = 440, solve l = 440 / (πr). With r a multiple of 7, π = 22/7 simplifies nicely to an integer value for l.

Step-by-Step Solution:Denominator πr = (22/7) * 14 = 44l = 440 / 44 = 10 cm

Verification / Alternative check:Plugging back: πrl = (22/7) * 14 * 10 = 440 cm^2, exact match.

Why Other Options Are Wrong:11, 12, 13, 14 cm do not satisfy πrl = 440 with r = 14; only 10 cm does.

Common Pitfalls:Using πr^2 (area of circle) instead of πrl; confusing height with slant height.

Final Answer:10 cm