An umbrella has 8 ribs which are equally spaced (see Fig.). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

We know that,  formula for the area of the sector of a circle

Area of the sector = $\frac{\theta }{{360}^0}$ $\times$ ${\mathrm{\pi r}}^2$

By observing the figure, we see that there are 8 equal ribs in an umbrella 

Thus, the angle between 2 consecutive ribs =  $\theta$ = 360⁰/8 = 45⁰

So, here the umbrella forms flat circle

Now, the radius of the flat circle = r = 45 cm 

Therefore, The area between 2 consecutive ribs of the umbrella = Area of a sector with an angle of 45⁰ = $\frac{\theta }{{360}^0}$ $\times$ ${\mathrm{\pi r}}^2$

=45⁰/360⁰ $\times$ 22/7 $\times$ 45  $\times$ 45 

= 1/8 $\times$ 22/7 $\times$ 45  $\times$45 

= 22275/28 

= 795.535 cm²