Question

An umbrella has 8 ribs which are equally spaced (see Fig. 11.10). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

Answer 1

There are 8 ribs in an umbrella. 

The area between two consecutive ribs is subtending \(\frac{360^{\degree}}8\) = \(45 ^{\degree}\) at the centre of the assumed flat circle.

Area between two consecutive ribs of circle = \(\frac{45^{\degree}}{ 360^{\degree}} \times \pi r^2\) = \(\frac18 \times \frac{22}7 \times (45)^2\)

                                                                      = \(\frac{11}{28} \times 2025\) = \(\frac{22275 }{28}\, cm^2\)