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Answer :
The circumference of the circle is 206.66 inches.
Given that an arc with a measure of 59 degrees has a length of 34π inches. We have to find the circumference of the
circle. To find the circumference of a circle we will use the formula: Circumference of a circle = 2πr, Where r is the
radius of the circle. A circle has 360 degrees. If an arc has x degrees, then the length of that arc is given by: Length of
arc = (x/360) × 2πr, Given that an arc with a measure of 59 degrees has a length of 34π inches34π inches = (59/360) ×
2πr34π inches = (59/360) × (2 × 22/7) × r34π inches = 0.163 × 2 × 22/7 × r34π inches = 1.0314 × r r = 34π/1.0314r =
32.909 inches. Now, we can calculate the circumference of the circle by using the formula of circumference.
Circumference of a circle = 2πr= 2 × 22/7 × 32.909= 206.66 inches (approx). Therefore, the circumference of the circle
is 206.66 inches.
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