4MA1/1H Jan 2023, Question 20: Stationary Points and Turning Points
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
A cylinder has radius x cm and height 800/(πx) − x cm. Its volume is V cm³. Determine the greatest possible V, rounded to the nearest whole number.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Height = 800 ÷ (πx) − x
- 2V = πx² × (800 ÷ (πx) − x)
- 3V = 800x − πx³
- 4dV/dx = 800 − 3πx²
- 5At the maximum, 800 − 3πx² = 0
- 6x² = 800 ÷ (3π) = 84.88...
- 7x = √84.88... = 9.213...
- 8V = 800 × 9.213... − π × 9.213...³
- 9V = 7370.5... − 2456.8... = 4913.6...
- 10V = 4914
Answer4914
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