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1. What is the measure in radians for the central angle of a circle whose radius is 6 cm and intercept arc length is 5.4 cm?

Make sure to show all calculations.

 

2. In a circle with a radius of 26.9 m, an arc is intercepted by a central angle of 9π/5 radians.

What is the arc length?

Use 3.14 for π and round your final answer to the nearest hundredth.

Make sure to show your calculations. 

Guest Feb 27, 2018
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4+0 Answers

 #1
avatar+12266 
+1

Circumference = pi * d   = pi * 2r = 12pi   cm

there are 2pi radians in a complete circle of which this Q is seekong a fraction

   5.4 / 12 pi =  ?/(2 pi)       ? = .9 radians

ElectricPavlov  Feb 27, 2018
 #2
avatar+26678 
0

By definition the angle in radians is simply the arc length divided by the radius.  

Alan  Feb 27, 2018
 #4
avatar+12266 
0

Thanx, Alan....good to remember...and simpler!

ElectricPavlov  Feb 27, 2018
 #3
avatar+12266 
+1

There are 2 pi radians in a complete circle

 

pi x 2r = circumference

pi x 2 x 26.9 =169 cm

 

 

fraction of this circumference intercepted by this central angle

 

?/169 = 9pi/5  /  2pi

?= 152.1 m

ElectricPavlov  Feb 27, 2018
edited by Guest  Feb 27, 2018

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