WAEC 2019 Mathematics · Question 35
The total surface area of a solid cylinder 165cm. Of the base diameter is 7cm, calculate its height. [Take ]
Options
- A.7.5 cm
- B.4.5 cm
- C.4.0 cm
- D.2.0 cm
Answer: C. 4.0 cm
Explanation written with AI and checked against the answer key
Analyze the question: A solid cylinder has total surface area 165 cm² and base diameter 7 cm. We need its height. Concept: For a solid cylinder, the total surface area includes the curved surface and both circular ends: TSA = 2πr² + 2πrh = 2πr(r + h) Solution: Radius r = 7 ÷ 2 = 3.5 cm Base area (both ends): 2πr² = 2 × (22/7) × 3.5² = 2 × (22/7) × 12.25 = 77 cm² The curved surface area is then: 165 − 77 = 88 cm² Curved surface area = 2πrh: 2 × (22/7) × 3.5 × h = 22h So 22h = 88, which gives h = 4 cm. Check: 2πr(r + h) = 22 × (3.5 + 4) = 22 × 7.5 = 165 ✓ Answer: The height is 4.0 cm, which is option C. Tip: Always check whether the question says "solid" (include both circular ends) or "open" (include only one end or none). Also, convert diameter to radius first. Many students lose marks by using 7 instead of 3.5. Plugging your answer back into the formula is a quick way to confirm it.AI can make mistakes. Report anything that looks wrong.
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