4MA1/2H Jan 2020, Question 26: Volume and Surface Area of a Cone
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks
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The question, in short
A sector AOB with angle x° forms the curved surface of a cone of height 25 cm and volume 1600 cm³; find x to the nearest whole number.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Volume: ⅓ × π × r² × 25 = 1600, so r² = 192/π and r = 7.817…
- 2Slant height l = √(7.817…² + 25²) = 26.19…
- 3Arc AB = base circumference: (x/360) × 2π × l = 2π × r
- 4x = 360 × r ÷ l = 360 × 7.817… ÷ 26.19… = 107.4…
- 5x = 107
Answer107
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