# An umbrella has 8 ribs which are equally spaced.

Question:

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

Solution:

Here, radius (r) = 45 cm

Since circle is divided in 8 equal parts,

$\therefore$ Sector angle corresponding to each part

$\theta=\frac{\mathbf{3 B 0}^{\circ}}{\mathbf{8}}=45^{\circ}$

$\Rightarrow$ Area of a sector (part)

$=\frac{\theta}{\mathbf{3 6 0}^{\circ}} \times \pi \mathbf{r}^{\mathbf{2}}=\frac{\mathbf{4 5}^{\circ}}{\mathbf{3 6 0}^{\circ}} \times \frac{\mathbf{2 2}}{\mathbf{7}} \times 45 \times 45 \mathrm{~cm}^{2}$

$=\frac{11 \times 45 \times 45}{4 \times 7} \mathrm{~cm}^{2}=\frac{22275}{28} \mathrm{~cm}^{2}$

$\therefore$ The required area between the two ribs

$=\frac{22275}{28} \mathrm{~cm}^{2}$