4MA1/1HR Jan 2020, Question 20: Frustum of a Cone
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Similar cones form a frustum with small cone height h and large cone height 2h, base radius r; sphere radius r. Given equal volumes, find r in terms of h in simplest form.
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Solution · 5 marks
- 1Volume of large cone = (1/3) × π × r² × 2h = (2/3)πr²h
- 2Volume of small cone = (1/3) × π × (r/2)² × h = (1/12)πr²h
- 3Volume of frustum = (2/3)πr²h − (1/12)πr²h = (7/12)πr²h
- 4Volume of sphere = (4/3)πr³
- 5(7/12)πr²h = (4/3)πr³
- 6Divide both sides by πr²: (7/12)h = (4/3)r
- 7Multiply both sides by 12: 7h = 16r
- 8r = 7h/16
Answer7h/16
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