The area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of 6π. The estimated value of π is 3.14.
is there a question somewhere in there?
You can start off by noting that
√(78.5/π) ≈ 5
To find the radius of the circle, we can use the formula for the area of a circle:
Area = π * r^2
Given that the area of the circle is 78.5 square centimeters, we can rearrange the formula to solve for the radius (r):
r = √(Area / π)
Substituting the given values:
r = √(78.5 / π)
≈ √(78.5 / 3.14)
≈ √(25)
≈ 5
So the radius of the circle is approximately 5 centimeters.
To find the circumference of the circle (which is the arc length for a full circle), we can use the formula:
Circumference = 2πr
Substituting the radius we found above:
Circumference = 2 * 3.14 * 5
≈ 31.4
Since the arc length subtends an angle less than a full circle, we can calculate the length of the subtending arc using the proportion:
Arc Length / Circumference = Angle / 360
Given that the arc length is 6π and the circumference is approximately 31.4:
6π / 31.4 = Angle / 360
Cross multiplying:
Angle = (6π * 360) / 31.4
≈ 689.17 degrees
So the estimated angle subtended by the arc on the circle is approximately 689.17 degrees.