Question

The angle of a sector in a given circle is $40$ degrees and the area of the sector is equal to $20c{m}^2$. Calculate the arc length of the sector.

• A. $6.5$ cm
• B. $7.4$ cm
• C. $5.3$ cm
• D. none of these

Answer 1

The correct option is C $5.3$ cm

Formula of area of sector = $\pi r^2\frac{\theta }{{360}^{\circ }}$; where $\theta$ is angle in degrees.

Given

angle of a sector in a circle ${40}^{\circ }$

area of the sector =$20{cm}^2$

therefore , $\pi r^2\frac{\theta }{{360}^{\circ }}$=$20{cm}^2$

$\pi r^2\frac{{40}^{\circ }}{{360}^{\circ }}=20$ [Here $\theta$ is ${40}^{\circ }$]

$r^2=\frac{180}{\pi }$

$r=\sqrt{57.3248}$

$r=7.57cm$

formula to find arc length of a sector=$2\pi r\frac{\theta }{{360}^{\circ }}$ [Here $\theta$ is ${40}^{\circ }$ and $r$ is $7.57cm$]

therefore

Arc length of a sector = $2\pi \left(7.57\right)\frac{{40}^{\circ }}{{360}^{\circ }}=5.28cm$

Arc length of a sector =5.3cm

option C is the answer.