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Twenty metres of wire is available for f...

Twenty metres of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in `s qdotm)` of the flower-bed is: (1) 25 (2) 30 (3) 12.5 (4) 10

A

30

B

12.5

C

10

D

25

Text Solution

Verified by Experts

The correct Answer is:
4
Total length `r+r+rtheta=2theta`
`rarr theta =(20-2r)/(r )` ltbvrgt Therefore area of flower bed

`A=1/2r^(2)theta =1/2r^(2)(20-2r)/(r )`
`rarr A=10r-r^(2)=25-(r-5)^(2)`
`therefore A_(max)`=25 (when r=5)
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