4MA1/2H Jan 2019, Question 22: 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
Cone with base diameter AB and vertex V; base area to total surface area ratio is 3:8. Find angle AVB in degrees to 1 decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Base area = πr², total surface area = πr² + πrl
- 28πr² = 3(πr² + πrl), so 5r² = 3rl
- 3So r/l = 3/5
- 4sin(½ AVB) = r/l = 3/5, so ½ AVB = 36.86…°
- 5Angle AVB = 2 × 36.86… = 73.7°
Answer73.7
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