Circles: Circumference and Area of a Circle

More Examples of Areas of Sectors

Let’s work through a couple more examples finding area of a sector.

Example:
Find the area of a sector with measure 200° in a circle with diameter 40 cm.

Circle with diameter 40 centimeters, 200 degrees sector is shaded.
Circle with radius 40 centimeters

Solution:
r=1/2d=1/2(40)=20
area of sector = arc measure/360 * A; area of sector = arc measure/360 *pi squared; area of sector = 200 / 360 * pi(20)squared = 2000/9 pi congruent to 698.13

The area of the sector is approximately 698.13 cm2.

Example:
Find the area of two-thirds of a circle with radius 15 m.

Circle with radius 15 meters, two-thirds of the circle is shaded.
Circle with radius 15 meters

Solution:
A = πr2 = π(15)2 = 225π m2.
Multiply the fraction by the area. 2/3(225pi) = 150pi
The area of two-thirds of a circle with radius 15 m is 150π m2.

 

Example:
Find the arc measure of the sector with radius 12 and area 10π ft2.

Solution:
In this problem, we are given the area of the sector and asked to find the arc measure.  Use a variable ‘x’ in place of the arc measure and solve for x.

area of sector = arc measure/360 * A; area of sector = arc measure/360 *pi squared; 10pi = x/360 * pi(12) squared; 10pi = 144pi/360 *x; 360/144pi * 10pi = 360/144pi * 144pi/360x; 25=x

The arc measures 25°.