Question

Find the length of the arc of a circle with radius of 20 centimeters intercepted by a central angle of 45 degrees

Answer 1

If the radius is 20cm, the circumference is

$C = 2\pi r = 40\pi$ centimeters.

Now, 45° is one eighth of a whole turn, so the arc intercepted by a 45° angle is one eighth of the whole circumference, so the answer is

$\dfrac{40\pi}{8} = 5\pi$