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Answer :
Final answer:
To find the radius of the given circle, we can use the formulas for the area of a sector and the length of an arc. By plugging in the given values and solving the equations, we find that the radius is approximately 2.6 inches.
Explanation:
To find the radius of a circle whose sector area is 59 square inches and whose arc measures 40 degrees, we can use the formulas for the area of a sector and the length of an arc:
Area of sector = (Arc Length / 360) x π x Radius^2
Length of arc = (π x Diameter x Arc Length) / 360
Given that the sector area is 59 square inches and the arc measure is 40 degrees, we can plug these values into the formulas and solve for the radius:
59 = (40/360) x π x Radius^2
Length of arc = (π x Diameter x 40) / 360
Simplifying these equations, we find that the radius is approximately 2.6 inches. Therefore, the correct answer is C) 2.6 inches.
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