JEE Mains · Maths · STD 12 - 6. Application of derivatives
Twenty metres of wire is available for fencing off a flowerbed in the form of a circular sector. Then the maximum area (in sq. m) of the flower bed is :
- A \(30\)
- B \(12.5\)
- C \(10\)
- D \(25\)
Answer & Solution
Correct Answer
(D) \(25\)
Step-by-step Solution
Detailed explanation
We have Total length \( = r + r + r\theta = 20\) \( \Rightarrow 2r + r\theta = 20\) \( \Rightarrow \theta = \frac{{20 - 2r}}{r}\) \(A = Area = \frac{\theta }{{2\pi }}\pi {r^2} = \frac{1}{2}{r^2}\theta = \frac{1}{2}{r^2}\left( {\frac{{20 - 2r}}{r}} \right)\) \(A = 10r - {r^2}\)…
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