Circumference of a circle

I just have a little question that i have read in the book of Thomas/Finney Calculus 9th edition that the circumference of a circle is 2pi,i can be wrong obviously but wasn't it supposed to be 2*pi*radius of the circle?

berkeman
Mentor
I just have a little question that i have read in the book of Thomas/Finney Calculus 9th edition that the circumference of a circle is 2pi,i can be wrong obviously but wasn't it supposed to be 2*pi*radius of the circle?
Both are correct if the radius r = 1. Can you scan the page in question and UPLOAD it?

Shafia Zahin
Math_QED
Homework Helper
2019 Award
Most likely, they calculated the length of the curve ##y = \sqrt{1 - x^2}##. This is the unit circle with radius ##1## and thus the circumference is equal to ##2\pi##.

If they would have calculated the length of the curve ##y = \sqrt{r^2 - x^2}##, the circumference would be equal to ##2\pi r##. This is the circle through the origin with radius ##r##.

Shafia Zahin
Both are correct if the radius r = 1. Can you scan the page in question and UPLOAD it?
Most likely, they calculated the length of the curve ##y = \sqrt{1 - x^2}##. This is the unit circle with radius ##1## and thus the circumference is equal to ##2\pi##.

If they would have calculated the length of the curve ##y = \sqrt{r^2 - x^2}##, the circumference would be equal to ##2\pi r##. This is the circle through the origin with radius ##r##.
Oh, yes, thank you, they have said about the unit circle at first then said that it's circumference is 2pi. Sorry,I didn't notice . But thank you again, I was really confused.