Question

Need help please its my last question

Answer 1

Given:

Radius of circle = 12 units

Area of sector = 24π sq. units.

Central angle = x

To find:

The value of x.

Solution:

We have,

$r=12$

$A=24\pi$

$\theta = x$

We know that, area of a sector is

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

Where, $\theta$ is central angle, r is radius.

$24\pi=\dfrac{x}{360^\circ}\pi (12)^2$

$24\pi=\dfrac{x}{360^\circ}\pi (144)$

$\dfrac{24\pi}{144\pi}=\dfrac{x}{360^\circ}$

$\dfrac{1}{6}=\dfrac{x}{360^\circ}$

Multiply both sides by 360 degrees.

$\dfrac{1}{6}\times 360^\circ=x$

$60^\circ=x$

The value of x is 60 degrees.

Therefore, the correct option is A.