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 120 cm2 . If it creates a new box using a scale factor of 3/4, determine the surface area of the new box. Round to the nearest tenth if necessary. (1 point)

Answer 1

When the scale factor of a box is changed, the surface area changes by the square of the scale factor.

In this case, the scale factor is \( \frac{3}{4} \). To find the new surface area, we can follow these steps:

1. Calculate the square of the scale factor: \[ \left( \frac{3}{4} \right)^2 = \frac{9}{16} \]

2. Multiply the original surface area by this factor: \[ \text{New Surface Area} = \text{Original Surface Area} \times \left( \frac{9}{16} \right) \] \[ \text{New Surface Area} = 120 , \text{cm}^2 \times \frac{9}{16} \]

3. Calculate the new surface area: \[ 120 , \text{cm}^2 \times \frac{9}{16} = 120 \times 0.5625 = 67.5 , \text{cm}^2 \]

Thus, the surface area of the new box is \( 67.5 , \text{cm}^2 \).