Find the area of each circular segment to the nearest tenth, given its central angle, x, and the radius of the circle.
x= pi/8, r=7
find the area of the whole circle pi r^2
multiply that by (central angle)/2pi
In this case:
Atotal = pi (49)
so the area of this fraction of the circle is
[(pi/8)/2pi ]pi (49)
=(49/16)pi
To find the area of a circular segment, we need to know the central angle (x) and the radius of the circle (r). The formula to find the area of a circular segment is:
A = (1/2) * r^2 * (θ - sin(θ))
In this case, the central angle (x) is given as π/8, and the radius (r) is given as 7. Let's plug these values into the formula to find the area.
A = (1/2) * 7^2 * (π/8 - sin(π/8))
First, let's calculate sin(π/8) using a calculator:
sin(π/8) ≈ 0.3827
Now we can substitute the values into the formula:
A ≈ (1/2) * 7^2 * (π/8 - 0.3827)
A ≈ (1/2) * 49 * (π/8 - 0.3827)
A ≈ 24.5 * (π/8 - 0.3827)
A ≈ 24.5 * (0.3927 - 0.3827)
A ≈ 24.5 * 0.01
A ≈ 0.245
Therefore, the area of the circular segment to the nearest tenth is approximately 0.2.