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Find the area of a circle whose circumference is 44cm44\,\text{cm} ?\newline15.4cm215.4\,\text{cm}^2\newline153cm2153\,\text{cm}^2\newline155cm2155\,\text{cm}^2\newline154cm2154\,\text{cm}^2\newline

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Q. Find the area of a circle whose circumference is 44cm44\,\text{cm} ?\newline15.4cm215.4\,\text{cm}^2\newline153cm2153\,\text{cm}^2\newline155cm2155\,\text{cm}^2\newline154cm2154\,\text{cm}^2\newline
  1. Recall Circle Circumference Formula: Recall the formula for the circumference of a circle. The formula for the circumference CC of a circle is C=2πrC = 2\pi r, where rr is the radius of the circle.
  2. Solve for Radius: Solve for the radius rr using the given circumference.\newlineGiven C=44cmC = 44\,\text{cm}, we can rearrange the formula to solve for rr: r=C2πr = \frac{C}{2\pi}.
  3. Calculate Radius: Calculate the radius.\newliner=44cm2π44cm6.28327cmr = \frac{44 \, \text{cm}}{2\pi} \approx \frac{44 \, \text{cm}}{6.2832} \approx 7 \, \text{cm} (rounded to the nearest whole number for simplicity).
  4. Recall Circle Area Formula: Recall the formula for the area AA of a circle.\newlineThe formula for the area of a circle is A=πr2A = \pi r^2.
  5. Calculate Area: Calculate the area using the radius. A=π(7cm)23.1416×49cm2153.9384cm2A = \pi(7 \, \text{cm})^2 \approx 3.1416 \times 49 \, \text{cm}^2 \approx 153.9384 \, \text{cm}^2.
  6. Round Area: Round the area to the nearest whole number.\newlineThe area of the circle, rounded to the nearest whole number, is approximately 154cm2154\,\text{cm}^2.