Curved surface area of a cone (approximate): A cone has base diameter 6 cm (r = 3 cm) and altitude 4 cm. Find its curved surface area approximately (in cm^2).

Introduction / Context:The curved (lateral) surface area of a right circular cone equals πrl, where l is the slant height. Given r and vertical height h, compute l from the Pythagorean relation l = √(r^2 + h^2) and then substitute into πrl. This is a classic 3-4-5 triangle scenario.

Given Data / Assumptions:

• Diameter = 6 cm → r = 3 cm
• Height h = 4 cm
• l = √(r^2 + h^2) = √(9 + 16) = √25 = 5 cm
• CSA = πrl

Concept / Approach:Substitute r and l directly into πrl. Since options are approximate integers, evaluate with π ≈ 3.14 and round to the closest option.

Step-by-Step Solution:CSA = π * 3 * 5 = 15π ≈ 47.1 cm^2Rounded → 47 cm^2

Verification / Alternative check:With π = 22/7, CSA = 15 * 22/7 ≈ 47.14, still rounds to 47 cm^2, confirming the choice.

Why Other Options Are Wrong:45 and 49 bracket but do not match the precise 47.1; 51 is too high; 43 is too low for l = 5 cm and r = 3 cm.

Common Pitfalls:Using base area πr^2 or total surface area instead of curved area; miscomputing l (it is 5 by the 3-4-5 triangle).

Final Answer:47 cm2