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A circle has an arc of length 24π that is intercepted by a central angle of 80°.

What is the radius of the circle?

 

How to do I go about this?

Guest Mar 30, 2017
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2+0 Answers

 #1
avatar+4157 
+3

arc length = radius * angle measured in radians

 

Convert 80º to radians.

80º * (π / 180º) rad. = 4π / 9 rad.

 

24π = radius * 4π / 9

54 = radius

hectictar  Mar 30, 2017
 #2
avatar+89781 
+3

A circle has an arc of length 24π that is intercepted by a central angle of 80°.

What is the radius of the circle?

 

The circumference of a circle is \(2\pi r\)

 

You have

 

 \(\frac{80}{360} \text{ of the circle}\\ so\\ \frac{80}{360}*2\pi r = 24\pi\\ \frac{8}{36}*2 r = 24\\ \frac{4}{9}* r = 24\\ r = 24*\frac{9}{4}\\ r =54\;units\)

 

check

80/360*2*pi*54 = 75.3982236861550377

24*pi = 75.3982236861550377           laugh

Melody  Mar 30, 2017

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