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Find the area of a circle with a circumference of 50.24 units. units ^(2)

Find the area of a circle with a circumference of 5050.2424 units.\newline□\square units 2 ^{2}

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Full solution

Q. Find the area of a circle with a circumference of 5050.2424 units.\newline□\square units 2 ^{2}
  1. Find Radius from Circumference: Use the circumference to find the radius of the circle.\newlineThe formula for the circumference CC of a circle is C=2πrC = 2\pi r, where rr is the radius.\newlineWe can rearrange this formula to solve for rr: r=C2πr = \frac{C}{2\pi}.\newlineGiven C=50.24C = 50.24 units, we can calculate rr as follows:\newliner=50.242πr = \frac{50.24}{2\pi}
  2. Calculate Radius: Calculate the radius.\newliner=50.242×3.14159r = \frac{50.24}{2 \times 3.14159}\newliner≈50.246.28318r \approx \frac{50.24}{6.28318}\newliner≈8r \approx 8 units (rounded to two decimal places for simplicity)
  3. Find Area from Radius: Use the radius to find the area of the circle.\newlineThe formula for the area AA of a circle is A=πr2A = \pi r^2.\newlineNow that we have the radius, we can calculate the area:\newlineA=π×(8)2A = \pi \times (8)^2
  4. Calculate Area: Calculate the area.\newlineA=3.14159×64A = 3.14159 \times 64\newlineA≈201.06A \approx 201.06 units2^2

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