Why does the book say circumference is 2π instead of 2πr?

[Shafia Zahin]

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?
Please help.

 

[berkeman]

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?
Please help.

Both are correct if the radius r = 1. Can you scan the page in question and UPLOAD it?

 

[member 587159]

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.