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 = $\frac{45^{\degree}}{ 360^{\degree}} \times \pi r^2$ = $\frac18 \times \frac{22}7 \times (45)^2$

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