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
305.3 in.2
305.3 in. squared
1,831.8 in.2
1 comma 831 point 8 in. squared
915.9 in.2
915.9 in. squared
395,668.8 in.2
Responses
305.3 in.2
305.3 in. squared
1,831.8 in.2
1 comma 831 point 8 in. squared
915.9 in.2
915.9 in. squared
395,668.8 in.2
Answers
GPT-4o mini
When a figure is dilated by a scale factor \( k \), the surface area of the new figure is \( k^2 \) times the surface area of the original figure.
In this case, the scale factor \( k = 6 \). Therefore, the relationship between the original surface area \( A \) and the dilated surface area \( A' \) can be expressed as:
\[
A' = k^2 \cdot A
\]
Given that the dilated surface area is \( A' = 10,990.8 \, \text{in}^2 \):
\[
10,990.8 = 6^2 \cdot A
\]
\[
10,990.8 = 36 \cdot A
\]
To find the original surface area \( A \), divide the dilated surface area by 36:
\[
A = \frac{10,990.8}{36} \approx 305.3 \, \text{in}^2
\]
Thus, the surface area of the original figure is **305.3 in.²**.
In this case, the scale factor \( k = 6 \). Therefore, the relationship between the original surface area \( A \) and the dilated surface area \( A' \) can be expressed as:
\[
A' = k^2 \cdot A
\]
Given that the dilated surface area is \( A' = 10,990.8 \, \text{in}^2 \):
\[
10,990.8 = 6^2 \cdot A
\]
\[
10,990.8 = 36 \cdot A
\]
To find the original surface area \( A \), divide the dilated surface area by 36:
\[
A = \frac{10,990.8}{36} \approx 305.3 \, \text{in}^2
\]
Thus, the surface area of the original figure is **305.3 in.²**.