Find the area of the curved surface of a cone whose base radius is 3cm and whose height is 4cm (π = 3.14)

Analyze the question: We need the curved surface area of a cone with base radius r = 3 cm and vertical height h = 4 cm. The formula uses the slant height, not the vertical height, so we must find the slant height first.

Concept:

• Curved surface area of a cone = πrl, where l is the slant height.
• The radius, height and slant height form a right-angled triangle, so l² = r² + h².

Solution:

Step 1: Find the slant height

l² = 3² + 4² = 9 + 16 = 25

l = 5 cm (this is the 3-4-5 triangle)

Step 2: Apply the formula

Curved surface area = πrl = 3.14 × 3 × 5 = 3.14 × 15 = 47.1 cm²

Answer: Option C (47.1 cm²).

Tip: Watch out for the common mistake of using the vertical height (4) in place of the slant height (5). That would give 3.14 × 3 × 4 = 37.68, which is close to option D and is a trap. Whenever you see radius 3 and height 4, remember the 3-4-5 triple, so the slant height is 5. Also remember: curved surface = πrl, total surface = πrl + πr².