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 find the surface area of the new box when the dimensions are scaled by a factor of \( \frac{1}{34} \), you can use the following relationship:

When the dimensions of a 3D object are scaled by a factor \( k \), the surface area is scaled by a factor of \( k^2 \).

In this case, the scale factor is \( \frac{1}{34} \). Thus, the surface area will be scaled by:

\[ k^2 = \left(\frac{1}{34}\right)^2 = \frac{1}{1156} \]

Now, to determine the surface area of the new box, you multiply the original surface area by \( \frac{1}{1156} \):

\[ \text{New Surface Area} = \text{Original Surface Area} \times k^2 = 112 , \text{cm}^2 \times \frac{1}{1156} \]

Calculating this:

\[ \text{New Surface Area} = \frac{112}{1156} \approx 0.0967 , \text{cm}^2 \]

Rounding to the nearest tenth:

\[ \text{New Surface Area} \approx 0.1 , \text{cm}^2 \]

Thus, the surface area of the new box is approximately 0.1 cm².