Question

A dilated figure has a surface area of 10,990.8 in.^2. The figure was dilated by a scale factor of 6. What is the surface area of the original figure?
A. 915.9 in.^2
B. 395,668.8 in.^2
C. 305.3 in.^2
D. 1,831.8 in.^2

Answer 1

When a figure is dilated by a scale factor \( k \), its surface area changes by a factor of \( k^2 \). In this case, the scale factor is \( 6 \). Therefore, the surface area of the original figure can be found using the formula:

\[
\text{Original Surface Area} = \frac{\text{Dilated Surface Area}}{k^2}
\]

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

\[
k^2 = 6^2 = 36
\]

Next, we can find the original surface area:

\[
\text{Original Surface Area} = \frac{10,990.8}{36}
\]

Now we perform the division:

\[
\text{Original Surface Area} = 305.3 \, \text{in}^2
\]

Therefore, the surface area of the original figure is:

\[
\boxed{305.3 \, \text{in}^2}
\]

So the correct answer is C. 305.3 in².