To find the area of the dilated circle, we first need to determine the radius of the dilated circle.
The original circle has a radius of 3 cm. When dilated with a scale factor of 3, the new radius becomes:
\[ \text{New radius} = \text{Original radius} \times \text{Scale factor} = 3 , \text{cm} \times 3 = 9 , \text{cm} \]
Next, we calculate the area of the dilated circle using the formula for the area of a circle:
\[ \text{Area} = \pi r^2 \]
Where \( r \) is the radius of the circle. Plugging in the new radius:
\[ \text{Area} = \pi (9 , \text{cm})^2 = \pi \times 81 , \text{cm}^2 \]
Using the approximate value of \( \pi \approx 3.14 \):
\[ \text{Area} \approx 3.14 \times 81 , \text{cm}^2 \approx 254.34 , \text{cm}^2 \]
Rounding this to the nearest tenth gives:
\[ \text{Area} \approx 254.3 , \text{cm}^2 \]
Therefore, the area of the dilated circle is approximately 254.3 square centimeters.
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