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 cm?. 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 calculate the surface area of the new box after applying the scale factor of \( \frac{3}{4} \), we use the relationship between the scale factor and the change in surface area.

The surface area of a three-dimensional object scales with the square of the scale factor. If we denote the scale factor as \( k \), then:

\[ \text{New Surface Area} = \text{Original Surface Area} \times k^2 \]

In this case, \( k = \frac{3}{4} \), and the original surface area is \( 112 , \text{cm}^2 \).

First, we calculate \( k^2 \):

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

Next, we calculate the new surface area:

\[ \text{New Surface Area} = 112 , \text{cm}^2 \times \frac{9}{16} \]

Now we perform the multiplication:

\[ \text{New Surface Area} = 112 \times \frac{9}{16} \]

Calculating the fraction:

\[ \frac{112}{16} = 7 \]

Then, multiply by 9:

\[ 7 \times 9 = 63 \]

Thus, the surface area of the new box is:

\[ \text{New Surface Area} = 63 , \text{cm}^2 \]

So, after rounding, the surface area of the new box is \( \boxed{63.0} , \text{cm}^2 \).

Answer 2

Wgats the answer

Answer 3

The surface area of the new box, after applying a scale factor of \( \frac{3}{4} \) to the original box with a surface area of \( 112 , \text{cm}^2 \), is \( 63 , \text{cm}^2 \).