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circle sector problem 2

exercise: circle sector problem 2


A circular sector has a central angle of 124° and an area of 44,82 cm²

a) calculate the radius

b) calculate the arc length

c) calculate the the perimeter/circumference of the circle sector 

 

answer: circle sector problem 2


a) answer radius

44.82 = r² * π * 124 : 360   / * 360
 
16 135.20 = r² * π * 88    / : 88
 
183.45… = r² * π    / : π
 
58.36 = r²    / √
 
r = 7.64 cm
 
A: The radius is 7.64 cm.

 

b) answer arc length
 
diameter (d) = 2 * 7.64  ⇒ 15.28 cm
 
arc length = d * π * α : 360  
 
arc length = 15.28 * π * 124 : 360
 
arc length = 16.53 cm
 
A: The arc length is 16.53 centimeter.

 

c) answer perimeter
 
perimeter = 2 * radius + arc length
 
perimeter = 2 * 7.64 + 16.53
 
perimeter = 31.81 cm
 
A: The perimeter of the circle is 31.81 centimeter.