To find the area of a circle given its circumference \( C = 4x \), we can follow these steps:
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Use the formula for the circumference of a circle: \[ C = 2\pi r \] Given that \( C = 4x \), we can set up the equation: \[ 4x = 2\pi r \]
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Solve for the radius \( r \): Divide both sides by \( 2\pi \): \[ r = \frac{4x}{2\pi} = \frac{2x}{\pi} \]
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Use the formula for the area of a circle: \[ A = \pi r^2 \] Substitute the expression for \( r \): \[ A = \pi \left(\frac{2x}{\pi}\right)^2 \]
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Simplify the area: \[ A = \pi \left(\frac{4x^2}{\pi^2}\right) = \frac{4x^2}{\pi} \]
Therefore, the area of the circle in terms of \( x \) is: \[ A = \frac{4x^2}{\pi} \]