The radius of a circle is 17.5 cm.

Question:

The radius of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44 cm in length.

Solution:

Given:
Radius = 17.5 cm
Length of the arc = 44 cm

Now,

Length of the arc $=\frac{2 \pi \mathrm{r} \theta}{360}$

$\Rightarrow 44=2 \times \frac{22}{7} \times 17.5 \times \frac{\theta}{360}$

$\Rightarrow \theta=\frac{44 \times 7 \times 360}{44 \times 17.5}$

 

$\Rightarrow \theta=144^{\circ}$

Also,

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

$=\frac{22}{7} \times 17.5 \times 17.5 \times 144$

 

$=385 \mathrm{~cm}^{2}$

 

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