What is the area of a sector of a circle of radius 5 cm

Question:

What is the area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm?

Solution:

We have

$r=5 \mathrm{~cm}$

length of the $\operatorname{arc}(l)=3.5 \mathrm{~cm}$

Now we will find the area of the sector.

Area of the sector $=\frac{1}{2} \times l r$

Substituting the values we get,

Area of the sector $=\frac{1}{2} \times 3.5 \times 5$...(1)

Now we will simplify the equation (1) as below,

Area of the sector $=\frac{1}{2} \times 17.5$

Area of the sector $=8.75$

Therefore, area of the sector is $8.75 \mathrm{~cm}^{2}$

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