What is the radius of a circle whose circumference is ##16π##?

##8##

The circumference of a circle is equal to ##pi##, which is a number ##~~3.14##, multiplied by the diameter of the circle.

Therefore, ##C=pid##.

We know that the circumference, ##C##, is ##16pi##, so we can say that:

##16pi=pid##

We can divide both sides by ##pi## to see that ##16=d##.

We now know that the diameter of the circle is ##16##.

We also know that the diameter has twice the length of the radius.

In equation form: ##2r=d##

##2r=16##

##color(red)(r=8##

Note that since ##2r=d##, the equation ##C=2pir## holds and can be used in place of ##C=pid##.