Question

The length of an arc of a circle is 4 cm and its radius is 6 cm. Find the area of this sector of the circle ?

Answer 1

Given, arc of the circle $=4cm$

radius, $r=6cm$

Let, the centre angle $=\theta$

$\therefore \theta =\frac{lengthofthearc}{radiusofthecircle}=\frac{4}{6}=\frac{2}{3}$

Note that this value is in radians.

Now, we know that, the area of a sector that subtends an angle $\theta$ at the centre of the circle is $\frac{\theta }{{360}^0}\times \pi r^2$

where, $\theta$ is in degrees.

Here, $\theta$ is in radians

Hence, take the full angle as $2\pi$ instead of ${360}^0$.

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

$\Rightarrow \frac{\frac{2}{3}}{2\times \pi }\times \pi \times 6^2$

$\Rightarrow \frac{2}{3\times 2\times \pi }\times \pi \times 36$

$\Rightarrow \frac{36}{3}$

$\therefore$ Required area $=12{cm}^2$

Hence, the area of the sector is $12c{m}^2$