Question

Pleaseee Helpp. If the radius is 21 m and area of sector of the circle are 27.72 m2, calculate the angle at the centre of the circle.​

Answer 1

Given:

Radius of a circle = 21 m

Area of a sector of the circle = 27.72 m²

To find:

The angle at the center of the circle.​

Solution:

The area of a second is:

$A=\pi r^2\times \dfrac{\theta}{360^\circ}$

Where, r is the radius of the circle and $\theta$ is the central angle.

Putting $\pi=\dfrac{22}{7},\ r=21,\ A=27.72$ in the above formula, we get

$27.72=\dfrac{22}{7}\times (21)^2\times \dfrac{\theta}{360^\circ}$

$27.72=1386\times \dfrac{\theta}{360^\circ}$

$27.72=3.85^\circ \times \theta$

$\dfrac{27.72}{3.85^\circ }=\theta$

$7.2^\circ=\theta$

Therefore, the central angle of the sector is $7.2^\circ$.