Question

Find the area of the sector of a circle if the radius of the circle is 5 cm, and the length of the arc is 4 cm.

• A. $10{\text{cm}}^2$
• B. $5{\text{cm}}^2$
• C. $20{\text{cm}}^2$
• D. $15{\text{cm}}^2$

Answer 1

The correct option is A $10{\text{cm}}^2$

We know that,
$\text{Length of the arc}\left(l\right)=\frac{\theta }{{360}^{\circ }}\times 2\pi r\dots \left(i\right)$ where $\theta$ is the angle subtentded by the arc at the centre of the circle.

$\text{Area of the sector}\left(A\right)\text{=}\frac{\theta }{{360}^{\circ }}\times \pi r^2$
Multiply and divide with 2 on the R.H.S.
$\Rightarrow A=\frac{\theta }{{360}^{\circ }}\times 2\pi r^2\times \frac{1}{2}$
$\Rightarrow A=(\frac{\theta }{{360}^{\circ }}\times 2\pi r)\times r\times \frac{1}{2}$
$\Rightarrow A=l\times \frac{r}{2}\left(\text{from}\right(i\left)\right)$

Given, $l=4\text{cm},r=5\text{cm}$

$\therefore \text{Area of the sector}\left(A\right)=4\times \frac{5}{2}$
$=10$

Hence, the area of the sector is $10{\text{cm}}^2.$