What is the length of the arc?

Question

A circle has a radius of 4. An arc in this circle has a central angle of 288°. 

Either enter an exacts number in terms of π or use 3.14 for π and enter your answer as a decimal. 

Answer 1

Hi Alexis,

 

The arc is formed on the circle.

 

The proportion of the length of the arc, x, to the circumference of the circle will be equal to the proportion of the central angle it faces to 360 degrees. Then, we can write

 

x                      288

------------ =  ----------

2*3.14*4          360

 

360x = 288*2*3.14*4

x = 20.1 units (rounded to the nearest tenth)