Question

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

• A. 8 m
• B. 5 m
• C. 2 m
• D. 4 m

Answer 1

Answer: (B)

5 m

Answer 2

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