To find the area of the dilated circle, we first need to determine the new radius after dilation.
The original radius of the circle is 3 cm. When we dilate this circle using a scale factor of 3, the new radius can be calculated as follows:
\[ \text{New radius} = \text{Original radius} \times \text{Scale factor} = 3 , \text{cm} \times 3 = 9 , \text{cm} \]
Next, we can calculate the area of the circle using the formula for the area of a circle:
\[ \text{Area} = \pi r^2 \]
where \( r \) is the radius of the circle. Substituting the new radius into the formula gives:
\[ \text{Area} = \pi (9 , \text{cm})^2 = \pi \times 81 , \text{cm}^2 \]
Calculating this gives:
\[ \text{Area} \approx 3.14159 \times 81 \approx 254.47 , \text{cm}^2 \]
Rounding this value to the nearest tenth, we find:
\[ \text{Area} \approx 254.5 , \text{cm}^2 \]
Thus, the area of the dilated circle is approximately 254.5 square centimeters.
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