20 meters of wire is available to fence of a flowerbed in the form of a circular sector. If the flowerbed is to have maximum surface area, then the radius of the circle is
20 meters of wire is available to fence of a flowerbed in the form of a circular sector. If the flowerbed is to have maximum surface area, then the radius of the circle is
- 8 m
- 5 m
- 2 m
- 4 m
The Correct Option is B
Solution and Explanation
Sector of a circle = 2l+r
2r+l = 20
l = 20 -2r
Area = \(\frac {1}{2}\)lr
Area = \(\frac {1}{2}\)*(20-2r)*r = 10r - r2
Now
dA/dx = 10 - 2r
10 - 2r = 0
r = 5 m
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Concepts Used:
Maxima and Minima
What are Maxima and Minima of a Function?
The extrema of a function are very well known as Maxima and minima. Maxima is the maximum and minima is the minimum value of a function within the given set of ranges.
There are two types of maxima and minima that exist in a function, such as:
- Local Maxima and Minima
- Absolute or Global Maxima and Minima