A sector of a circle with diameter 8 meters has an area of 18 meters squared. What is the central angle of that sector?
[18 / (π r^2)] * 360º
1/2 r^2 θ = area
1/2 * 16 θ = 18
θ = 9/4
To find the central angle of a sector, you need to use the formula that relates the angle to the area of the sector and the radius of the circle.
The formula to find the area of a sector is A = (θ/360) * π * r^2, where A is the area of the sector, θ is the central angle (in degrees), π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
In this case, the diameter of the circle is given as 8 meters. The radius can be found by dividing the diameter by 2: r = 8 / 2 = 4 meters.
You are also given that the area of the sector is 18 square meters: A = 18 square meters.
Plugging these values into the formula, we have:
18 = (θ/360) * π * 4^2
Simplifying further:
18 = (θ/360) * 16π
Now, we can solve for θ by isolating it.
Divide both sides of the equation by 16π:
(θ/360) = 18 / (16π)
Multiply both sides of the equation by 360:
θ = (18 / (16π)) * 360
Using a calculator, evaluate the right side of the equation:
θ = (18 / (16π)) * 360 ≈ 114.59
Therefore, the central angle of the sector is approximately 114.59 degrees.