Circumference & Arc Measure: Is this Correct?

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SUMMARY

The discussion centers on the relationship between circumference, arc measure, and angles in a circle. The formula for circumference, given by C = 2πr, is correctly identified, but there is confusion regarding the conversion between degrees and arc length. Specifically, the arc measure for a 70-degree angle with a radius of 10 should be calculated as (7π/18) * 10, not (7/18)π. This highlights the importance of maintaining consistent units when performing calculations involving angles and lengths.

PREREQUISITES
  • Understanding of circle geometry, including radius and circumference
  • Familiarity with the relationship between degrees and radians
  • Knowledge of arc length formulas
  • Basic algebra skills for solving equations
NEXT STEPS
  • Study the derivation of the arc length formula in circles
  • Learn how to convert between degrees and radians effectively
  • Explore the properties of circles and their geometric relationships
  • Practice solving problems involving arc measures and circumferences
USEFUL FOR

Students studying geometry, educators teaching circle properties, and anyone looking to solidify their understanding of arc measures and circumference calculations.

Miike012
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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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360° ≡ 2π

In your working you equated 360 to 2πr meaning that you equated degrees to a length, which is incorrect.
 
isnt the equation for circumference 2(pi)r?
and circumference refers to the entire circle which is 360 deg.
 
Well...
 
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.
 
that's exactly right except that the arc length should be (7pi/18)(10) not (7/18)pi
 

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