To find the area of a circle when given the circumference, we can follow these steps:
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Use the circumference formula: The circumference \( C \) of a circle is given by the formula: \[ C = 2\pi r \] where \( r \) is the radius.
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Solve for the radius: Given that the circumference is \( 22\pi \): \[ 22\pi = 2\pi r \]
Divide both sides by \( 2\pi \): \[ r = \frac{22\pi}{2\pi} = 11 \text{ inches} \]
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Use the area formula: The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \]
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Substitute the radius into the area formula: \[ A = \pi (11)^2 = \pi \times 121 \]
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Substitute \( \pi = 3.14 \): \[ A = 3.14 \times 121 \]
Now, calculate the area: \[ A = 3.14 \times 121 = 380.94 \]
So, the area of the circle is 380.94 square inches (expressed to the hundredths place).