Question

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)
cm2

Answer 1

When scaling the dimensions of a box by a factor, the surface area changes by the square of that scale factor.

Given:
- Original surface area = 120 cm²
- Scale factor = \( \frac{3}{4} \)

To find the new surface area, we calculate the square of the scale factor:

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

Now, we multiply the original surface area by the square of the scale factor:

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

Calculating this:

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

So, the surface area of the new box is **67.5 cm²**.