Find the area of a sector of a circle with a radius of 3 m and a central angle of 125degrees.
Area K = 1/2 r^2 * angle in rads
Convert deg to rads
125 deg * pi/180 = 25pi/36 rads
K = 1/2 * 3^2 * 25pi/36
K = ? m^2
you do the math
Area K is expressed in m^2 (in this case)
area of whole circle = 9π
area of sector = (125/360)(9π) = appr. 9.8 m^2
Area of circle:
A=r^2*pi
Area of your sector=r^2*pi*(125/360)=3^2*pi*125/360=9*pi*125/360
=9*3.1415926535*125/360
=3534,2917351875/360
=9,8174770421875 m^2
To find the area of a sector of a circle, you need to use the formula:
Area of sector = (θ/360) * π * r^2
Where:
θ is the central angle in degrees
π is a mathematical constant approximately equal to 3.14159
r is the radius of the circle
Given values:
θ = 125 degrees
r = 3 m (radius)
Now, let's substitute the given values into the formula and calculate the area of the sector:
Area of sector = (125/360) * π * (3^2)
= (0.3472) * 3.14159 * (9)
≈ 9.061 square meters
Therefore, the area of the sector of the circle with a radius of 3 m and a central angle of 125 degrees is approximately 9.061 square meters.