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

To find the surface area of the new box after applying a scale factor, you can use the relationship between scale factors and surface area.

When a shape is scaled by a factor \( k \), the surface area will be scaled by \( k^2 \). In this case, the scale factor is \( \frac{3}{4} \).

First, we calculate the scale factor for the area:

\[ k = \frac{3}{4} \] \[ k^2 = \left(\frac{3}{4}\right)^2 = \frac{9}{16} \]

Next, we multiply the original surface area by this factor:

\[ \text{Original Surface Area} = 120 , \text{cm}^2 \] \[ \text{New Surface Area} = 120 , \text{cm}^2 \times \frac{9}{16} \]

Now, let's perform the multiplication:

\[ \text{New Surface Area} = 120 \times \frac{9}{16} = \frac{120 \times 9}{16} = \frac{1080}{16} = 67.5 , \text{cm}^2 \]

Therefore, the surface area of the new box is:

\[ \boxed{67.5} , \text{cm}^2 \]