Circumference & Arc Measure: Is this Correct?

In summary, the conversation discusses the formulas for circumference and arc measure of a circle, using examples of a circle with a radius of 10 and an angle measure of 70 degrees. The correct equations are given and clarified, with an emphasis on not equating degrees to a length.
  • #1
Miike012
1,009
0

Homework Statement


Just got done reading the chapter... Want to make sure I have this right...

IF Circumference = 2(pi)r
Let cir = 360 deg.
So that 360 deg = 2(pi)r

And 180 deg = (pi)r

IF r = 10
then 180 = (pi)10

Hence half of a cirlce with radius of 10 has an arc measure of 10(pi)...

Is this correct?


And if I wanted to find An arc measure of angle 70 deg I would
solve for x
180x = 70
x = 70/180 = 7/18
then
70 = (7/18)(Pi)(10)
If radius is 10...

Homework Equations





The Attempt at a Solution

 
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  • #2
360° ≡ 2π

In your working you equated 360 to 2πr meaning that you equated degrees to a length, which is incorrect.
 
  • #3
isnt the equation for circumference 2(pi)r?
and circumference refers to the entire circle which is 360 deg.
 
  • #4
Well...
 
  • #5
Miike012 said:
isnt the equation for circumference 2(pi)r?
and circumference refers to the entire circle which is 360 deg.

360 degrees would be the ratio of the circumference of the circle to its diameter.
 
  • #6
that's exactly right except that the arc length should be (7pi/18)(10) not (7/18)pi
 

1. What is circumference?

Circumference is the distance around a circle. It is measured by taking the length of the curved line that forms the circle.

2. How is circumference calculated?

The formula for calculating circumference is C = 2πr, where C is the circumference, π is the mathematical constant pi (approximately 3.14), and r is the radius of the circle. This formula can also be written as C = πd, where d is the diameter of the circle.

3. What is the difference between circumference and diameter?

Circumference is the distance around a circle, while diameter is the distance across the circle passing through its center. They are related by the formula C = πd, where C is the circumference and d is the diameter.

4. How do you measure arc length?

Arc length is measured in degrees or radians, depending on the unit of measure used for the circle's radius. To calculate arc length, use the formula L = rθ, where L is the arc length, r is the radius, and θ is the central angle in radians.

5. How is arc length related to circumference?

Arc length is a portion of the circumference of a circle. It is calculated by dividing the central angle by 360 degrees (or 2π radians) and multiplying by the circumference of the circle. In other words, the circumference is equal to the arc length when the central angle is 360 degrees or 2π radians.

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