I have a circle with a radius of 20in. Arc mEGF = 235(not shaded part of circle) find the area of arc EF (shaded sector of circle).
My answer was 82.3 in^2
correct answer is 436.3 in^2
I need disrection on this one- I was really off on my answer.
To find the area of the shaded sector EF, first we need to find its central angle, and then use the formula to find the area.
1. Central angle of arc EF = 360 - 235 = 125 degrees
2. Area of entire circle = π * r^2 = π * (20 in)^2 = 400π in^2
3. Area of shaded sector EF = (125/360) * 400π in^2 ≈ 436.3 in^2
So the correct answer is approximately 436.3 in^2.
To find the area of the shaded sector, we need to calculate the central angle of arc EF first.
We know that the entire circle has 360 degrees, and the measure of arc mEGF is 235. The central angle will be the same measure as the arc.
So, the central angle of arc EF = 235 degrees.
To find the area of the shaded sector, we will use the formula:
Area of sector = (angle / 360) * π * r^2
Where:
angle is the central angle in degrees
r is the radius of the circle
Plugging in the values, we get:
Area of sector = (235 / 360) * π * (20)^2
Calculating this, we get:
Area of sector = (0.6528) * 3.14159 * 400
Area of sector = 817.25 in^2
So, the correct answer for the area of arc EF is 817.25 square inches, not 436.3 square inches as mentioned earlier.
To find the area of a shaded sector of a circle, you need to use the formula:
Area of sector = (angle/360) * π * r^2
In this case, the given angle is 235 degrees, and the radius is 20 inches.
First, convert the angle from degrees to radians. Since there are 2π radians in a complete circle (360 degrees), you can use the conversion factor:
Angle in radians = (angle in degrees) * (π/180)
Angle in radians = 235 * (π/180) ≈ 4.099 radians
Next, substitute the values into the formula:
Area of sector = (4.099/2π) * π * 20^2
Simplifying the equation:
Area of sector ≈ (4.099/2) * (20^2)
Area of sector ≈ 2.0495 * 400
Area of sector ≈ 819.8 square inches
Therefore, the correct answer for the area of the shaded sector of the circle is approximately 819.8 square inches, not 436.3 square inches.