Question

A circle has a circumference of `3600pi` What is the diameter of the circle?

Answer 1

See a solution process below:

Explanation:

The formula for the circumference of a circle is:

`C = 2pir` or `C = 2rpi`

However, the relationship between the radius and diameter of a circle is:

`d = 2r`

So, we can also write the formula for the circumference of a circle as:

`C = dpi`

Substituting `3600pi` for `C` and solving for `d` gives:

`3600pi = dpi`

`(3600pi)/color(red)(pi) = (dpi)/color(red)(pi)`

`(3600color(red)(cancel(color(black)(pi))))/cancel(color(red)(pi)) = (dcolor(red)(cancel(color(black)(pi))))/cancel(color(red)(pi))`

`3600 = d`

`d = 3600`