Understanding the Circumference of a Circle: A Comparison of 2π and 2πr

In summary, the conversation discusses the calculation of the circumference of a circle and the difference between using the unit circle and a circle with a specific radius. The book mentions that the circumference of a unit circle is 2pi, but if the radius is not 1, the formula would be 2*pi*radius. The confusion is cleared up when considering the specific curves being calculated.
  • #1
Shafia Zahin
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1
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.
 
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  • #2
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.
Both are correct if the radius r = 1. Can you scan the page in question and UPLOAD it?
 
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  • #3
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##.
 
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  • #4
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##.

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.
 

What is the formula for finding the circumference of a circle?

The formula for finding the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle.

How is the circumference of a circle different from the diameter?

The circumference of a circle is the distance around the circle, while the diameter is the distance across the circle passing through its center. The circumference is always longer than the diameter and is equal to π times the diameter.

Can the circumference of a circle be negative?

No, the circumference of a circle cannot be negative. It is a measurement of distance and therefore can only be positive or zero.

What units are typically used for measuring the circumference of a circle?

The circumference of a circle is typically measured in units of length, such as centimeters, inches, or meters.

How is the circumference of a circle related to its area?

The circumference of a circle is related to its area through the formula C = πd, where d is the diameter of the circle. This means that the circumference is directly proportional to the diameter, while the area is proportional to the square of the diameter.

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