An arc of a circle has a measure of 80 degrees and a length of 88pi. What is the diameter of the circle?

Question

This a geometry word problem that i had trouble solving. 

Answer 1

80/360 of the circumference is two ninths of circumference; C = pi(diameter)

(2/9)(pi)(d) = 88(pi)

 

you can now solve for diameter d.

Answer 2

The perimeter of the whole circle is 2*pi*radius

 

The arc length is then:

80/360 * 2 * pi * radius = 88 * pi

 

80/180 * pi * radius = 88 * pi

 

80/180 * radius = 88

 

radius = 88 * 180 / 80

 

         = 44 * 180 / 40

 

         = 22 * 180 / 20

 

          = 11 * 180 / 10

 

          = 11 * 18

 

          = (10 + 1)*18

 

          = 180 + 18

 

           = 198

 

The diameter is 2 * 198 = 2 * (200 - 2) = 400 - 4 = 396

 

CHECK:

 

  Circumference = pi * diameter = pi * 396

 

  Arc Length = 80/360 * pi * 396 = 88*pi