To find the area of the dilated circle, we can follow these steps:
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Calculate the radius of the dilated circle: The original radius of the circle is 3 cm. If the circle is dilated using a scale factor of 3, the new radius will be: \[ \text{New radius} = \text{Original radius} \times \text{Scale factor} = 3 , \text{cm} \times 3 = 9 , \text{cm} \]
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Calculate the area of the dilated circle: The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] where \( r \) is the radius of the circle. Substituting the new radius into the formula gives: \[ A = \pi (9 , \text{cm})^2 = \pi \times 81 , \text{cm}^2 \]
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Calculate \( \pi \times 81 \): Using an approximation for \( \pi \) as \( 3.14 \): \[ A \approx 3.14 \times 81 \approx 254.34 , \text{cm}^2 \]
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Round the result to the nearest tenth: \[ A \approx 254.3 , \text{cm}^2 \]
Thus, the area of the dilated circle is approximately 254.3 square centimeters.