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)
cm2

Answer 1

To determine the surface area of the new box when the original box's surface area is given and a scale factor is applied, we can use the formula for scaling surface area.

When the dimensions of a three-dimensional object are scaled by a factor of \( k \), the surface area is scaled by a factor of \( k^2 \).

In this case, the original surface area is \( 112 \, cm^2 \) and the scale factor provided is \( \frac{3}{4} \).

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

2. Next, multiply the original surface area by this scaling factor:
\[
\text{New Surface Area} = 112 \, cm^2 \times \frac{9}{16}
\]

3. Performing the multiplication:
\[
112 \times \frac{9}{16} = \frac{112 \times 9}{16} = \frac{1008}{16} = 63
\]

Therefore, the surface area of the new box is \( 63 \, cm^2 \).

Thus, the answer is:
\[
\text{Surface area of the new box: } 63 \, cm^2
\]