When a three-dimensional object is dilated using a scale factor \( k \), its surface area changes according to the square of the scale factor.
Given the original surface area \( A \) of the cylinder is 54 cm², and the scale factor \( k \) is \( \frac{1}{2} \), the surface area \( A' \) of the new cylinder can be calculated as follows:
\[ A' = A \cdot k^2 \]
Substituting the values:
\[ A' = 54 , \text{cm}^2 \cdot \left(\frac{1}{2}\right)^2 \] \[ A' = 54 , \text{cm}^2 \cdot \frac{1}{4} \] \[ A' = \frac{54}{4} , \text{cm}^2 = 13.5 , \text{cm}^2 \]
Therefore, the surface area of the new cylinder after dilation is 13.5 cm².
The correct answer is 3. 13.5 cm².