Question

the area of the shaded circular sector is equal to 30. The radius of the circle is 10. Find the measure of the central angle (in degrees)

Answer 1

Given:

There are given that the area of the shaded circular sector is:

$30\pi$

Explanation:

To find the central angle, we need to use the formula of area of the sector:;

So,

From the formula of area of the sector:

$Area\text{ of sector=}\frac{central\text{ angle}}{360^{\circ}}\times\pi r^2$

Then,

Put the value of area and radius into the above formula;

So,

$\begin{gathered} Area\text{ of sector=}\frac{central\text{ angle}}{360^{^{\circ}}}\times\pi r^2 \\ 30\pi=\frac{centralangle}{360}\pi\times(10)^2 \end{gathered}$

Then,

$\begin{gathered} 30\pi=\frac{centralangle}{360}\pi(10)^{2} \\ 3=\frac{centralangle}{36} \\ central\text{ angle=36}\times3 \\ central\text{ angle=108}^{\circ} \end{gathered}$

Final answer:

hence, the central angle is 108 degrees.