When a shape is dilated using a scale factor, the surface area changes by the square of that scale factor.
In this case, the scale factor is \( \frac{1}{3} \). To find the new surface area, we can apply the scale factor to the original surface area of 486 in².
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First, find the square of the scale factor: \[ \left(\frac{1}{3}\right)^2 = \frac{1}{9} \]
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Then multiply the original surface area by this value: \[ \text{New Surface Area} = \text{Original Surface Area} \times \frac{1}{9} \] \[ \text{New Surface Area} = 486 \times \frac{1}{9} = 54 \text{ in.}^2 \]
Thus, the new surface area after dilation is \( 54 \text{ in.}^2 \).
The correct response is 54 in.².