Question

Assume the radius of a circle is

unit

What is the area of the circle? What is the circumference?

How many radii are needed to wrap completely around the circle? Express your answer as a decimal approximation and as an exact value.

Does the size of the circle matter? That is, does the number of radii needed to wrap completely around the circle change as the radius of the circle gets larger or smaller? Why does this make sense?

Exactly how many radians are in
? In

Answer 1

Explanation:

They want you to see how radius is important. Just remember that one radian is one radius, that should help you see why radius is important.

They ask for the unit circle , that is a circle of one unit for the radius, which makes it super easy to calculate things for it, they ask what is the area, which is that famous formula, π
`r^(2)` , then they ask what's its circumference. which is that other famous formula 2πr

so to go all the way around a circle of one unit radius, it's 2π exactly or about 6.28..... units, call it meters, or feet or inches, it doesn't mater here.

the size of the circle doesn't matter here either, b/c we are using the radius , that relaationship doesn't change , all circles, what ever size , have this same relationship between the radius and radians. :P this is handy.