Calculate the area of sector of a circle which subtends an angel of 45°at the center of the circle, radius 14cm. Solve this please.
The area of the circle:
A = r² π
The area of sector of a circle:
As = r² π ∙ θ / 360°
In this case:
As = 14² π ∙ 45° / 360° = 196 π ∙ 45° / 45° ∙ 8 = 196 π / 8 =
4 ∙ 49 π / 4 ∙ 2 = 49 / 2 π = 49 ∙ 3.14159 / 2 = 76.968955
As = 76.97 cm²
rounded on two decimal places
OR
45° / 360° = 1 / 8
As = 1 / 8 A = 1 / 8 r² π = 1 / 8 14² π = 196 ∙ 3.14159 / 8 = 76.968955
As = 76.97 cm²
rounded on two decimal places
Calculate the atra of a sector of a cicle which subtends an angle of 45 at the centre of the cicle,radius 14
solve
To calculate the area of a sector, you can use the formula:
Area of sector = (θ/360) x πr^2
where θ is the angle in degrees and r is the radius of the circle.
Given that the angle at the center is 45° and the radius is 14 cm, we can substitute these values into the formula:
Area of sector = (45/360) x π(14^2)
First, calculate the value inside the parentheses:
45/360 = 0.125
Next, calculate the value of π(14^2):
π(14^2) = 3.14 x (14^2) = 3.14 x 196 = 615.44
Now, substitute the values into the formula:
Area of sector = 0.125 x 615.44
To calculate this, simply multiply 0.125 by 615.44:
Area of sector = 76.93 cm^2
Therefore, the area of the sector is 76.93 square centimeters.