Question

Find the length of an arc of 40° in a circle with an 8 inch radius. 8/9 inches 16/9 inches 64/9 inches

Answer 1

To understand how to obtain arc length, you have to understand first that the ratio between the arc length and the circumference is equal to the ratio between the angle that forms that arc length and 360 degrees(a full circle).

So, the equation for arc length is the following:

`(s)/(2\pi r)= (x)/(360)`
Where s is the arc length, r is the radius, and x is the angle.

So just substitute the information in the question into the equation:

`(s)/(2\pi *8)= (40)/(360) \\ \\ (s)/(16\pi)= (1)/(9) \\ \\ s= (16\pi)/(9) inches`