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.

Explanation-

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

Area of the sector = θ/360⁰ × πr²

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

Thus, the angle between 2 consecutive ribs = θ = 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 = θ3600 × πr2

=45⁰/360⁰ × 22/7 × 45 × 45 

= 1/8 × 22/7 × 45 ×45 

= 22275/28 

= 795.535 cm²