Find the area of a sector of a circle of radius 14cm which subtend an angle 280
Area of a circle = r² π
Area of a sector of a circle = r² π ∙ θ / 360°
In this case:
A = r² π ∙ 280 / 360 = 14² π ∙ 280 / 360 =
196 π ∙ 40 ∙ 7 / 40 ∙ 9 = 196 π ∙ 7 / 9 = 1372 π / 9 =
1372 ∙ 3.1416 / 9 = 4310.2752 / 9 = 478.91946 ≈ 479 cm²
≈ means approximately equal
To find the area of a sector of a circle, you can use the formula:
Area of Sector = (Angle/360) * π * r^2
where:
Angle is the measure of the angle subtended by the sector
r is the radius of the circle
In this case, the radius (r) is given as 14cm and the angle (Angle) is 280 degrees.
Firstly, we convert 280 degrees to radians by multiplying by π/180:
Angle in radians = 280 * (π/180)
= (28/18) * π
= (14/9) * π
Next, we substitute the values into the formula:
Area of Sector = ((14/9) * π / 360) * π * (14^2)
= (14/9) * π * π/360 * 196
= (14/9) * (π^2/360) * 196
= (14 * π^2 * 196) / (9 * 360)
= (14 * 3.14 * 196) / 9
= 615.44 cm^2
Therefore, the area of the sector of a circle with a radius of 14cm and an angle of 280 degrees is 615.44 cm^2.
To find the area of a sector of a circle, you can use the formula:
Area = (θ/360) * π * r^2
Where:
- θ is the angle in degrees that the sector subtends.
- π is a mathematical constant approximately equal to 3.14159.
- r is the radius of the circle.
In this case, the radius (r) is given as 14 cm, and the angle (θ) is given as 280 degrees.
Let's substitute these values into the formula to find the area:
Area = (280/360) * π * (14)^2
First, we simplify the fraction:
Area = (7/9) * π * (14)^2
Next, we calculate the square of 14:
Area = (7/9) * π * 196
Finally, we multiply the remaining numbers:
Area ≈ (7/9) * 3.14159 * 196 ≈ 449.648 cm^2
Therefore, the area of the sector of the circle is approximately 449.648 square centimeters.