To find the area of the dilated circle, we first need to determine the radius of the dilated circle. The original radius of the circle is 3 cm, and since the photocopier dilates it with a scale factor of 3, we can calculate the new radius as follows:
\[ \text{New radius} = \text{Original radius} \times \text{Scale factor} = 3 , \text{cm} \times 3 = 9 , \text{cm} \]
Next, we use the formula for the area of a circle, which is given by:
\[ \text{Area} = \pi r^2 \]
Substituting the new radius into the formula:
\[ \text{Area} = \pi (9 , \text{cm})^2 = \pi (81 , \text{cm}^2) = 81\pi , \text{cm}^2 \]
Now, we can approximate the value of \(\pi\) as 3.14. Therefore:
\[ \text{Area} \approx 81 \times 3.14 = 254.34 , \text{cm}^2 \]
Finally, rounding this value to the nearest tenth gives us:
\[ \text{Area} \approx 254.3 , \text{cm}^2 \]
Thus, the area of the dilated circle is approximately 254.3 square centimeters.
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