Question

A circle has a radius of 6 in.

What is the exact length of an arc formed by a central angle measuring 45°?



Enter your answer in the box. Express your answer using π .

in.

Answer 1

`(3\pi )/(2)`

Proof (Picture):

Answer 2

This is the concept of perimeter of circles, the arc length of the circle will be given by:
(theta)/360*pi*diameter
diameter=2*radius
but;
radius=6 in
diameter=2*6=12 inches
theta=45°
Hence, the arc length will be:
45/360*π*12
=(3π)/2