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
915.9 in.2
915.9 in. squared
305.3 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
915.9 in.2
915.9 in. squared
305.3 in.2
Answers
GPT-4o mini
When a figure is dilated by a scale factor \( k \), the surface area of the dilated figure is related to the original surface area \( A \) by the formula:
\[
\text{Surface Area of Dilated Figure} = k^2 \times A
\]
In your case, the surface area of the dilated figure is \( 10,990.8 \, \text{in}^2 \), and the scale factor \( k \) is 6. We can rearrange the formula to find the surface area of the original figure:
\[
A = \frac{\text{Surface Area of Dilated Figure}}{k^2}
\]
Substituting the values:
\[
A = \frac{10,990.8 \, \text{in}^2}{6^2} = \frac{10,990.8 \, \text{in}^2}{36}
\]
Calculating \( A \):
\[
A = \frac{10,990.8}{36} \approx 305.3 \, \text{in}^2
\]
So, the surface area of the original figure is \( 305.3 \, \text{in}^2 \).
The correct response is:
**305.3 in.²**
\[
\text{Surface Area of Dilated Figure} = k^2 \times A
\]
In your case, the surface area of the dilated figure is \( 10,990.8 \, \text{in}^2 \), and the scale factor \( k \) is 6. We can rearrange the formula to find the surface area of the original figure:
\[
A = \frac{\text{Surface Area of Dilated Figure}}{k^2}
\]
Substituting the values:
\[
A = \frac{10,990.8 \, \text{in}^2}{6^2} = \frac{10,990.8 \, \text{in}^2}{36}
\]
Calculating \( A \):
\[
A = \frac{10,990.8}{36} \approx 305.3 \, \text{in}^2
\]
So, the surface area of the original figure is \( 305.3 \, \text{in}^2 \).
The correct response is:
**305.3 in.²**