In a circle of radius $ 35 \mathrm{~cm} $, an arc subtends an angle of $ 72^{\circ} $ at the centre. Find the length of the arc and area of the sector.

Given:

Radius of the circle $r=35 \mathrm{~cm}$.

Angle subtended by the arc $=72^{\circ}$

To do:

We have to find the length of the arc and area of the sector.

Solution:

Let the length of the arc be $l$.

We know that,

Length of arc $=2 \pi r(\frac{\theta}{360^{\circ}})$

Therefore,

Length of the arc $l=2 \times \pi \times 35 \times \frac{72^{\circ}}{360^{\circ}} \mathrm{cm}$

$=70 \pi \times \frac{1}{5} \mathrm{cm}$

$=14 \pi \mathrm{cm}$

$=14 \times \frac{22}{7} \mathrm{cm}$

$=44 \mathrm{~cm}$

Area of the sector $=\pi r^{2} \times \frac{\theta}{360^{\circ}}$

$=\frac{22}{7}(35)^{2} \times \frac{72^{\circ}}{360^{\circ}}$

$=\frac{22}{7} \times 35 \times 35 \times \frac{1}{5}$

$=770 \mathrm{~cm}^{2}$

The length of the arc and area of the sector are $44 \mathrm{~cm}$ and $770 \mathrm{~cm}^{2}$ respectively.

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Updated on: 10-Oct-2022

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