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

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Given:

An umbrella has 8 ribs which are equally spaced.

Radius of the circle $= 45\ cm$

To do:

We have to find the area between the two consecutive ribs of the umbrella.

Solution:

Radius of the circle $= 45\ cm$

Number of ribs $= 8$

Angle between two consecutive ribs $=\frac{\text { Central angle of the circle }}{\text { Number of ribs }}$

$=\frac{360^{\circ}}{8}$

$=45^{\circ}$

Area between two consecutive ribs $=$ Area of one sector of the circle

$=\frac{\pi r^{2} \theta}{360^{\circ}}$

$=\frac{22}{7} \times \frac{45 \times 45 \times 45^{\circ}}{360^{\circ}}$

$=\frac{11 \times 45 \times 9 \times 5}{7 \times 4}$

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

The area between the two consecutive ribs of the umbrella is $\frac{22275}{28} \mathrm{~cm}^{2}$.

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Updated on: 10-Oct-2022

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