Question

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is:

• A. $12.5$
• B. $10$
• C. $25$
• D. $30$

Answer 1

The correct option is C $25$

Length of wire$=r(\theta +2)=20m\text{Area A}=\frac{\theta }{2}{r}^2\Rightarrow A\left(r\right)=10r-r^2\text{Area is maximum if r =}5.$
Maximum area $A=25$ sq. m