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 112 cm2
. If it creates a new box using a scale factor of 34
, 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, 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.