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

How to find Angle of Sector of a Circle if Diameter of Circle and Area of Sector are given

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 = `fractheta{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 = 9`pi` 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 = `fractheta{360}pi r^2`

9π = `fractheta{360}pi r^2`

θ = `frac{9times360}{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.