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The circle with center O has a circumference of 20 pi. What is the area of the shaded region?

The circle with center O O has a circumference of 20π 20 \pi . What is the area of the shaded region?

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Full solution

Q. The circle with center O O has a circumference of 20π 20 \pi . What is the area of the shaded region?
  1. Calculate Circumference: Circumference of the circle is given by C=2⋅π⋅rC = 2 \cdot \pi \cdot r, where rr is the radius.\newlineGiven C=20⋅πC = 20 \cdot \pi, we can solve for rr.
  2. Solve for Radius: 20×π=2×π×r20 \times \pi = 2 \times \pi \times r\newlineDivide both sides by 2×π2 \times \pi to find rr.\newliner=20×π2×πr = \frac{20 \times \pi}{2 \times \pi}
  3. Find Area Formula: Simplify the equation to find the radius. \newliner=202r = \frac{20}{2}\newliner=10r = 10
  4. Calculate Area: Now we have the radius, we can find the area of the circle using the formula A=π⋅r2A = \pi \cdot r^2.A=π⋅(10)2A = \pi \cdot (10)^2
  5. Calculate Area: Now we have the radius, we can find the area of the circle using the formula A=π⋅r2A = \pi \cdot r^2.A=π⋅(10)2A = \pi \cdot (10)^2Calculate the area.A=π⋅100A = \pi \cdot 100A=100⋅πA = 100 \cdot \pi

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