WAEC 2021 Mathematics · Question 12
A cone has a base radius of 8cm and height 11cm. calculate , correct to 2d.p, the curved surface area
Options
- A.341.98cm
- B.276.57cm
- C.201.14cm
- D.477.71cm
Answer: A. 341.98cm
Explanation written with AI and checked against the answer key
Analyze the question: We need the curved surface area of a cone with base radius r = 8 cm and vertical height h = 11 cm. Concept: Curved surface area = πrl, where l is the slant height. Because we are given the vertical height, we must first find l using Pythagoras' theorem: l² = r² + h² Step 1: Find the slant height l² = 8² + 11² = 64 + 121 = 185 l = √185 ≈ 13.6015 cm Step 2: Find the curved surface area CSA = πrl = π × 8 × 13.6015 8 × 13.6015 = 108.812 CSA = 3.14159 × 108.812 ≈ 341.84 cm² With π = 22/7: 22/7 × 108.812 = 341.98 cm². This matches option A exactly, so the examiners used π = 22/7. With π = 3.142 the result would be about 341.9, and with 3.14159 it is 341.84. Only option A is close to these, and it matches the π = 22/7 value exactly. Answer: A (341.98 cm²) Tip: When a cone question gives the vertical height, always find the slant height l = √(r² + h²) first. Do not plug h directly into πrl. Also, if an answer is slightly different from yours, check whether the question expects π = 22/7 or 3.142. Here the options point to 22/7.AI can make mistakes. Report anything that looks wrong.
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