How to Find Angle of Sector of a Circle by its Diameter and Sector Area

QUESTION: The diameter of a circle is 20 miles. What is the angle measure of an arc bounding a sector with an area of 9π miles² ?

SOLUTION:

The formula for

Area of a sector = $\frac\theta{360}\pi r^2$ ————————-(1)

where θ is the angle of the sector in degrees

and r is the radius of the circle

Here,

Area of the sector = 9π miles²

Diameter of a circle = 20 miles

So,radius of the circle = $\frac{Diameter}2$ = $\frac{20}2$ = 10 miles

we have to find θ

Put values in equation (1)

Area of a sector = $\frac\theta{360}\pi r^2$

9π = $\frac\theta{360}\pi r^2$

θ = $\frac{9\times360}{100}$

θ = 32.4 degrees

Thus if the diameter of a circle is 20 miles, area of a sector is 9 $\pi$ square miles then the angle of the sector is 32.4 degrees.

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