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The perimeter of a quarter circle is 7.147.14 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

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Full solution

Q. The perimeter of a quarter circle is 7.147.14 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
  1. Understand the problem: Step 11: Understand the problem. We need to find the radius of a quarter circle given its perimeter is 7.147.14 yards.
  2. Formula for perimeter: Step 22: Formula for the perimeter of a quarter circle is P=πd2+d P = \frac{\pi d}{2} + d , where d d is the diameter. Since the radius r r is half the diameter, d=2r d = 2r .
  3. Substitute diameter into formula: Step 33: Substitute d=2r d = 2r into the perimeter formula. So, P=π(2r)2+2r P = \frac{\pi (2r)}{2} + 2r . Simplify to P=πr+2r P = \pi r + 2r .
  4. Plug in values: Step 44: We know P=7.14 P = 7.14 yards and π≈3.14 \pi \approx 3.14 . Plug these values into the equation: 7.14=3.14r+2r 7.14 = 3.14r + 2r .
  5. Combine like terms: Step 55: Combine like terms: 7.14=5.14r 7.14 = 5.14r .
  6. Solve for radius: Step 66: Solve for r r : r=7.145.14 r = \frac{7.14}{5.14} .
  7. Calculate radius: Step 77: Calculate r r : r≈1.39 r \approx 1.39 yards.

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