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The perimeter of a quarter circle is 3.57 inches. What is the quarter circle's radius? Use pi~~3.14 and round your answer to the nearest hundredth. ◻ inches

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Answer

1.5

Explanation

The perimeter of a quarter circle is the sum of the length of the arc and the length of the radius. The length of the arc can be calculated using the formula (θ/360) * 2πr, where θ is the angle of the arc in degrees and r is the radius. In this case, the angle is 90 degrees (since it's a quarter circle), so the length of the arc is (90/360) * 2πr = πr/2. The length of the radius is r. Therefore, the perimeter of the quarter circle is πr/2 + r.Given that the perimeter is 3.57 inches and π is approximately 3.14, we can set up the equation 3.14r/2 + r = 3.57. Solving this equation for r gives r ≈ 1.5 inches. Therefore, the radius of the quarter circle is approximately 1.5 inches.

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