The radius of a circle is 6 centimeters. What is the length of a 150° arc?

Answer 1

The total circumfrence of a circle is determined by 2π * r

In this case, the radius (r) = 6. So, the total circumfrence of the circle is 2π(6) = 12π cm.

Next, we find what portion of the circle is being measured, and divide by the whole. In this case, working with degrees, we want to find the length of an arc 150 degrees. We divide 150 by 360, and multiply that answer by our total circumfrence (12π).

150/360 = 5/12.

(5/12) * (12π) = 5π cm

Answer 2

The circumference of the circle is the total length around the circle and is found using the equation

C = 2πr

This means for this circle, the total length around the circle is

C=2π(6cm)

C=12π cm

To find the length of this 150°arc, we can see that this is 150/360th of the circle because the circle contains 360°.

Therefore, to find the length of this arc we can take a fraction of the total length around the circle.

Length = 150/360 (C)

Length = 150/360 (12π cm)

Length = 5π cm

The length of the arc would be 5π cm

Answer 3

length = (150/360)(2 * π * 6)