Question

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

Answer 1

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.