Question

Select the correct option from the given alternatives :

20 metres of wire is available for fencing off a flower-bed in the form of a circular sector of radius 5 metres, then the maximum area (in sq. m.) of the flower-bed is

Options

• 15

• 20

• 25

• 30

Answer 1

25

Explanation:

r + r + rθ = 20m

∴ 2r + rθ = 20

∴ θ = ${\displaystyle \frac{20-2\text{r}}{\text{r}}}$

r = 5m

Area = ${\displaystyle \frac{1}{2}{\text{r}}^2\theta }$

= ${\displaystyle \frac{1}{2}{\text{r}}^2\left(\frac{20-2\text{r}}{\text{r}}\right)}$

= ${\displaystyle \frac{1}{2}{\left(5\right)}^2\left(\frac{20-10}{5}\right)}$

= 25 sq. m