A sector of a circle of radius 9 cm subtends angle 120 at center of the circle find the area of the sector to the nearest cm
To find the area of a sector, you can use the formula:
Area of a sector = (θ/360) * π * r^2
where θ is the angle in degrees and r is the radius of the circle.
Given:
Radius (r) = 9 cm
Angle (θ) = 120 degrees
Let's substitute these values into the formula:
Area of the sector = (120/360) * π * (9^2)
= (1/3) * π * 81
= (1/3) * 3.1416 * 81
= 84.78 cm^2
Therefore, the area of the sector is approximately 84.78 cm^2.
To find the area of the sector, you need to use the formula:
Area = (θ/360) * πr^2
Where:
- θ is the central angle of the sector in degrees
- r is the radius of the circle
In this case, the radius (r) is given as 9 cm, and the central angle (θ) is given as 120 degrees.
Substituting these values into the formula:
Area = (120/360) * π * 9^2
Simplifying further:
Area = (1/3) * π * 81
Area ≈ 84.78 cm^2
Therefore, the area of the sector is approximately 84.78 square centimeters when rounded to the nearest cm.
120/360 = 1/3
so
we want one third the area of the circle
(1/3) pi (81) =