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?(1 point)
Responses

1,831.8 in.2
1 comma 831 point 8 in. squared

305.3 in.2
305.3 in. squared

395,668.8 in.2
395 comma 668 point 8 in. squared

915.9 in.2

Answer 1

When a figure is dilated by a scale factor \( k \), the surface area of the dilated figure is scaled by a factor of \( k^2 \).

In this case, the scale factor is 6, so the surface area of the dilated figure is given by:

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

This means:

\[
10,990.8 = 6^2 \times \text{Original Surface Area}
\]

Calculating \( k^2 \):

\[
6^2 = 36
\]

So we have:

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

Now, to find the original surface area, we can divide both sides by 36:

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

Calculating this gives:

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

Thus, the surface area of the original figure is **305.3 in²**.

The correct response is:

**305.3 in.²**