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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)

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 class=

Sagot :

Given:

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

[tex]30\pi[/tex]

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:

[tex]Area\text{ of sector=}\frac{central\text{ angle}}{360^{\circ}}\times\pi r^2[/tex]

Then,

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

So,

[tex]\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}[/tex]

Then,

[tex]\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}[/tex]

Final answer:

hence, the central angle is 108 degrees.

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