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

An umbrella has 8 ribs.

The angle subtended at the center by the area between two consecutive ribs of the assumed flat circular umbrella is \( \frac{360^{\degree}}{8} = 45^{\degree} \).

The area between two consecutive ribs of the circle is \( \frac{45^{\degree}}{360^{\degree}} \times \pi r^2 = \frac{1}{8} \times \frac{22}{7} \times (45)^2 \)

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