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 395,668.8 in.2 395 comma 668 point 8 in. squared 915.9 in.2 915.9 in. squared 1,831.8 in.2
Answers
GPT-4o mini
To find the surface area of the original figure before dilation, you can use the property that the surface area of a dilated figure is equal to the surface area of the original figure multiplied by the square of the scale factor.
Let \( S_o \) be the surface area of the original figure, and the scale factor \( k = 6 \). The surface area of the dilated figure (\( S_d \)) is given as 10,990.8 in².
The formula to relate the original surface area to the dilated surface area is:
\[
S_d = k^2 \times S_o
\]
Substituting the known values into the formula:
\[
10,990.8 = 6^2 \times S_o
\]
Calculating \( 6^2 \):
\[
6^2 = 36
\]
Now, substituting that back into the equation:
\[
10,990.8 = 36 \times S_o
\]
To find \( S_o \), divide both sides by 36:
\[
S_o = \frac{10,990.8}{36} \approx 305.3
\]
So the surface area of the original figure is approximately 305.3 in².
The correct response is **305.3 in.²**.
Let \( S_o \) be the surface area of the original figure, and the scale factor \( k = 6 \). The surface area of the dilated figure (\( S_d \)) is given as 10,990.8 in².
The formula to relate the original surface area to the dilated surface area is:
\[
S_d = k^2 \times S_o
\]
Substituting the known values into the formula:
\[
10,990.8 = 6^2 \times S_o
\]
Calculating \( 6^2 \):
\[
6^2 = 36
\]
Now, substituting that back into the equation:
\[
10,990.8 = 36 \times S_o
\]
To find \( S_o \), divide both sides by 36:
\[
S_o = \frac{10,990.8}{36} \approx 305.3
\]
So the surface area of the original figure is approximately 305.3 in².
The correct response is **305.3 in.²**.