To find the surface area of the new box after applying a scale factor, we need to use the property that the surface area scales by the square of the scale factor.
Given:
- Original surface area = 112 cm²
- Scale factor = \(\frac{3}{4}\) or 0.75
To calculate the new surface area, we use the formula:
\[ \text{New Surface Area} = \text{Original Surface Area} \times \text{(Scale Factor)}^2 \]
Calculating \((\frac{3}{4})^2\):
\[ \left(\frac{3}{4}\right)^2 = \frac{9}{16} \]
Now, apply this to the original surface area:
\[ \text{New Surface Area} = 112 \times \frac{9}{16} \]
First, calculate \( \frac{112}{16} \):
\[ \frac{112}{16} = 7 \]
Now multiply by 9:
\[ \text{New Surface Area} = 7 \times 9 = 63 \text{ cm}^2 \]
Therefore, the surface area of the new box is 63.0 cm² when rounded to the nearest tenth.