The area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of 6pi. The estimated value of is 3.14.
what is the measure of the angle subtended by the arc in degrees?
since a=πr^2 = 78.5 = 25π, r=5
since s=rθ = 6π, θ = 6π/5 = 216°
To find the measure of the angle subtended by the arc, you can use the formula:
Angle subtended by arc = (Arc length / Circumference of the circle) * 360 degrees
First, let's calculate the circumference of the circle using the given area. The formula to find the circumference of a circle is:
Circumference = 2 * pi * radius
However, we are not given the radius directly. Instead, we are given the area of the circle. The formula to find the radius from the area is:
Radius = sqrt(Area / pi)
So, let's calculate the radius:
Radius = sqrt(78.5 / 3.14)
Radius = sqrt(25)
Radius = 5 cm
Now that we have the radius, we can calculate the circumference:
Circumference = 2 * pi * 5
Circumference = 10pi cm
Now, we can find the angle subtended by the arc:
Angle subtended by arc = (6pi / 10pi) * 360 degrees
Angle subtended by arc = 0.6 * 360 degrees
Angle subtended by arc = 216 degrees
Therefore, the measure of the angle subtended by the arc is 216 degrees.
To find the measure of the angle subtended by the arc in degrees, we need to use the formula:
Angle (in radians) = Arc Length / Radius
First, let's determine the radius of the circle using the formula for the area of a circle:
Area of a circle = π * radius^2
78.5 = 3.14 * radius^2
Dividing both sides by 3.14 to solve for the radius:
radius^2 = 78.5 / 3.14
radius^2 = 25
Taking the square root of both sides:
radius = √25
radius = 5 cm
Now, let's use the formula for the angle subtended by the arc:
Angle (in radians) = 6π / 5
To convert this to degrees, we use the formula:
Angle (in degrees) = Angle (in radians) * (180 / π)
Angle (in degrees) = (6π / 5) * (180 / π)
Angle (in degrees) = 6 * 180 / 5
Angle (in degrees) = 36 * 36
Angle (in degrees) = 216 degrees
Therefore, the measure of the angle subtended by the arc is 216 degrees.