Tick the correct answer in the following: Area of a sector of angle p (in degrees) of a circle with radius R is
(a) $\frac{p}{180^o} \times 2 \pi R$
(b) $\frac{p}{180^o} \times \pi R^2$
(c) $\frac{p}{360^o} \times 2 \pi R$
(d) $\frac{p}{720^o} \times 2 \pi R^2$

Given:

Angle of the sector $=p$

Radius of the circle $=R$

To do:

We have to find the area of the seactor.

Solution:

We know that,

Area of a sector $=\frac{\pi r^{2} \theta}{360^o}$

Here,
$\theta=p$ and radius $=\mathrm{R}$
Therefore,

Area of the sector $=\frac{\pi R^{2} p}{360^o}$

$=\frac{p}{360^o} \times \pi R^{2}$

Multiplying and dividing by 2, we get,

$=\frac{2}{2}\times\frac{p}{360^o} \times \pi R^{2}$

$=\frac{p}{720^o} \times 2 \pi R^{2}$

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Updated on: 10-Oct-2022

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