The circumference of a circle can be expressed as both 2π and 2πr, depending on the context. In the case of the unit circle, where the radius (r) is equal to 1, the circumference simplifies to 2π. For circles with a radius greater than 1, the correct formula is 2πr. This distinction is crucial for understanding the relationship between radius and circumference in different scenarios.
PREREQUISITESStudents of mathematics, educators teaching geometry and calculus, and anyone seeking clarity on the relationship between radius and circumference in circles.
Both are correct if the radius r = 1. Can you scan the page in question and UPLOAD it?Shafia Zahin said: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 said:Both are correct if the radius r = 1. Can you scan the page in question and UPLOAD it?
Math_QED said: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##.