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 395,668.8 in.2 395 comma 668 point 8 in. squared 305.3 in.2 305.3 in. squared 915.9 in.2
Answers
GPT-4o mini
When a figure is dilated by a scale factor of \( k \), the surface area of the new figure will be \( k^2 \) times the surface area of the original figure.
In this case, the scale factor \( k = 6 \), so \( k^2 = 6^2 = 36 \).
Let \( A \) be the surface area of the original figure. We know from the problem that the surface area of the dilated figure is \( 10,990.8 \) in². This gives us the equation:
\[
10,990.8 = 36A
\]
To find the surface area \( A \) of the original figure, we can solve for \( A \):
\[
A = \frac{10,990.8}{36}
\]
Calculating this:
\[
A = 305.3 \, \text{in}^2
\]
Thus, the surface area of the original figure is **305.3 in²**.
In this case, the scale factor \( k = 6 \), so \( k^2 = 6^2 = 36 \).
Let \( A \) be the surface area of the original figure. We know from the problem that the surface area of the dilated figure is \( 10,990.8 \) in². This gives us the equation:
\[
10,990.8 = 36A
\]
To find the surface area \( A \) of the original figure, we can solve for \( A \):
\[
A = \frac{10,990.8}{36}
\]
Calculating this:
\[
A = 305.3 \, \text{in}^2
\]
Thus, the surface area of the original figure is **305.3 in²**.