The surface area of a cube is given by the formula:
\[ \text{Surface Area} = 6s^2 \]
where \(s\) is the length of one side of the cube. When a cube is dilated by a scale factor \(k\), the side length of the new cube becomes \(ks\).
In this case, the scale factor is \(14\). Thus, the new side length of the cube after dilation is \(14s\).
The surface area of the dilated cube can be calculated as follows:
\[ \text{New Surface Area} = 6(14s)^2 = 6 \cdot 196s^2 = 1176s^2 \]
The surface area increases by the square of the scale factor (in this case, \(14^2 = 196\)):
\[ \text{New Surface Area} = 196 \times \text{Original Surface Area} \]
If you provide the original surface area of the cube, I can calculate the dilated cube's surface area for you. If it's not provided, the final expression considering the original surface area \(A\) would be:
\[ \text{New Surface Area} = 196A \]
Please provide the side length or the original surface area to get a specific numerical answer.
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