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

To maximize the area of a circular sector with a fixed perimeter, the formula for the area of the sector is given as \( A = \frac{r^2 \theta}{2} \), where \( r \) is the radius and \( \theta \) is the angle in radians. Since you have 20 meters of wire available as the arc length plus the two radii (which is a fixed 20 m), you would set up the relationship \( L = r\theta + 2r = 20 \) to find optimal values of \( r \) and \( \theta \). Solving these equations will lead you to redefine \( r \) in terms of \( \theta \) and maximize the area. When you perform the calculations, you would find that the maximum area occurs when \( \theta = \frac{3\pi}{2} \) radians, which gives you a maximum flower bed area of around 100 square meters! Now that's a blooming lovely garden space!