In a circle of radius 35 cm,


In a circle of radius 35 cm, an arc subtends an angle of 72° at the centre. Find the length of the arc and area of the sector.


We know that the arc length / and area $A$ of a sector of an angle $\theta$ in the circle of radius $r$ is given by $l=\frac{\theta}{360^{\circ}} \times 2 \pi r$ and $A=\frac{\theta}{360^{\circ}} \times \pi r^{2}$ respectively.

It is given that, $r=35 \mathrm{~cm}$ and $\theta=72^{\circ}$.

We will calculate the arc length using the value of r and θ,

$l=\frac{72^{\circ}}{360^{\circ}} \times 2 \pi \times 35 \mathrm{~cm}$

$=\frac{72^{\circ}}{360^{\circ}} \times 2 \times \frac{22}{7} \times 35 \mathrm{~cm}$

$=44 \mathrm{~cm}$

Now, we will find the value of area A of the sector

$A=\frac{72^{\circ}}{360^{\circ}} \times \pi \times 35 \times 35 \mathrm{~cm}^{2}$

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

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