To find the radius of a circle given its area, we can use the formula for the area of a circle:
\[ A = \pi r^2 \]
where:
- \( A \) is the area,
- \( r \) is the radius, and
- \( \pi \) is a constant approximately equal to 3.14159.
Given the area \( A = 1,809.56 \) square centimeters, we can rearrange the formula to solve for the radius \( r \):
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Start with the area formula: \[ A = \pi r^2 \]
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Substitute the value of \( A \): \[ 1,809.56 = \pi r^2 \]
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Divide both sides by \( \pi \): \[ r^2 = \frac{1,809.56}{\pi} \]
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Now, use \( \pi \approx 3.14159 \): \[ r^2 = \frac{1,809.56}{3.14159} \]
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Calculate the right side: \[ r^2 \approx \frac{1,809.56}{3.14159} \approx 575.38 \]
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Finally, take the square root of both sides to find \( r \): \[ r = \sqrt{575.38} \approx 24.0 \text{ cm} \]
So, the radius of the circle is approximately 24.0 centimeters.