To find the area of the dilated circle, we first need to determine the new radius after the dilation. The original radius of the circle is 3 cm, and it is dilated by a scale factor of 3.
\[ \text{New radius} = \text{Original radius} \times \text{Scale factor} = 3 , \text{cm} \times 3 = 9 , \text{cm} \]
Next, we calculate the area of the dilated circle using the formula for the area of a circle, which is:
\[ \text{Area} = \pi r^2 \]
Substituting the new radius into the formula:
\[ \text{Area} = \pi (9 , \text{cm})^2 = \pi \times 81 , \text{cm}^2 \approx 254.47 , \text{cm}^2 \]
Finally, rounding to the nearest tenth:
\[ \text{Area} \approx 254.5 , \text{cm}^2 \]
Thus, the area of the dilated circle is approximately 254.5 square centimeters.
1 answer