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The perimeter of a quarter circle is 10.7110.71 yards. What is the quarter circle's radius?\newline\newlineUse π≈3.14\pi \approx 3.14 and round your answer to the nearest hundredth.\newline____ yards\newline

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Q. The perimeter of a quarter circle is 10.7110.71 yards. What is the quarter circle's radius?\newline\newlineUse π≈3.14\pi \approx 3.14 and round your answer to the nearest hundredth.\newline____ yards\newline
  1. Calculate Perimeter of Full Circle: Calculate the perimeter of the full circle by multiplying the given perimeter of the quarter circle by 44. \newlinePerimeter of full circle = 4×10.714 \times 10.71 yards = 42.8442.84 yards.
  2. Find Radius Using Circumference Formula: Use the formula for the circumference of a circle, which is 2πr2\pi r, to find the radius. Set the full circle's perimeter equal to the circumference.\newline2πr=42.842\pi r = 42.84 yards.
  3. Solve for Radius: Solve for rr (radius) by dividing the circumference by 2π2\pi.\newliner=42.842×3.14r = \frac{42.84}{2 \times 3.14} = 66.8282 yards.

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