A laundry soap company decides it wants to shrink the size of its box to save on cost. The surface area of the original box is \( 112 \mathrm{~cm}^{2} \). If it creates a new box using a scale factor of \( \frac{3}{4} \), determine the surface area of the new box Ro \( \mathrm{cm}^{2} \)

To find the surface area of the new box, we use the property that when you scale the dimensions of a shape by a factor \( k \), the area scales by a factor of \( k^2 \). Here, the scale factor is \( \frac{3}{4} \). Calculating the area scaling factor: \[ \left(\frac{3}{4}\right)^2 = \frac{9}{16} \] Now, applying this scaling factor to the original surface area: \[ \text{New Surface Area} = 112 \, \text{cm}^2 \times \frac{9}{16} = 112 \times 0.5625 = 63 \, \text{cm}^2 \] Thus, the surface area of the new box is \( 63 \, \text{cm}^2 \).