To model the effect of a dilation on the area of a two-dimensional shape, we need to understand how dilation works. When a shape is dilated by a scale factor \( k \), the new area is given by the formula:
\[ \text{New Area} = k^2 \times \text{Original Area} \]
In this case, the scale factor is 3, so we calculate:
\[ \text{New Area} = 3^2 \times \text{Original Area} = 9 \times \text{Original Area} \]
This means that the area of the shape will become 9 times as great after the dilation.
Therefore, the correct response is:
The area will be 9 times as great.