If a central angle of measure 30 degree is subtended by a circular arc of length 6 meters how Many meters in length is the radius of a ciicle
To find the length of the radius of a circle, we can use the formula for the circumference of a circle:
C = 2πr
Given that a central angle of measure 30 degrees subtends a circular arc of length 6 meters, we know that this arc represents 30/360 = 1/12 of the entire circumference of the circle. Therefore, the entire circumference of the circle would be 12 times the length of the given arc:
C = 12 * 6 = 72 meters
Using the formula for circumference, we can solve for the radius:
C = 2πr
72 = 2πr
Divide both sides by 2π:
r = 72 / (2π) ≈ 11.46 meters
Therefore, the length of the radius of the circle is approximately 11.46 meters.