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circle sector problem 3

exercise: circle sector problem 3


A circular sector has central angle of 170° and an arc length of 15 m.

a) calculate the radius

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

c) calculate the the area of the circle sector

 

answer: circle sector problem 3


a) answer radius:
 
arc length = d * π * α : 360  
 
15 = d * π * 170 : 360   / * 360
 
5 400 = d * π * 170  / : 170
 
31.76… = d * π   / : π
 
10.11 = d     / : 2    
 
r = 5.06 m
 
A: The radius is 5.06 m.

 

b) answer perimeter:
 
perimeter = 2 * radius + arc length
 
perimeter = 2 * 5.06 + 15
 
perimeter = 25.12 m
 
A: The perimeter of the circle is 31.81 meters.

 

c) answer area:
 
area = r² * π * α : 360 
 
area = 5.06² * π * 170 : 360 
 
area = 37.98 m²
 
A: The area of the circle is 37.98 m².