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 395,668.8 in.2 395 comma 668 point 8 in. squared 1,831.8 in.2 1 comma 831 point 8 in. squared 915.9 in.2 915.9 in. squared 305.3 in.2
Answers
GPT-4o mini
To find the surface area of the original figure before dilation, we can use the formula that relates the surface areas before and after dilation using the scale factor. The surface area of a figure after dilation can be calculated using the equation:
\[
\text{Surface Area}_{\text{dilated}} = \text{Surface Area}_{\text{original}} \times (\text{scale factor})^2
\]
Given:
- Surface Area of the dilated figure = 10,990.8 in²
- Scale factor = 6
We can rearrange the equation to solve for the surface area of the original figure:
\[
\text{Surface Area}_{\text{original}} = \frac{\text{Surface Area}_{\text{dilated}}}{(\text{scale factor})^2}
\]
Now substituting the known values:
\[
\text{Surface Area}_{\text{original}} = \frac{10,990.8}{6^2} = \frac{10,990.8}{36}
\]
Calculating that gives:
\[
\text{Surface Area}_{\text{original}} = 305.3 \, \text{in}^2
\]
So the surface area of the original figure is **305.3 in²**.
\[
\text{Surface Area}_{\text{dilated}} = \text{Surface Area}_{\text{original}} \times (\text{scale factor})^2
\]
Given:
- Surface Area of the dilated figure = 10,990.8 in²
- Scale factor = 6
We can rearrange the equation to solve for the surface area of the original figure:
\[
\text{Surface Area}_{\text{original}} = \frac{\text{Surface Area}_{\text{dilated}}}{(\text{scale factor})^2}
\]
Now substituting the known values:
\[
\text{Surface Area}_{\text{original}} = \frac{10,990.8}{6^2} = \frac{10,990.8}{36}
\]
Calculating that gives:
\[
\text{Surface Area}_{\text{original}} = 305.3 \, \text{in}^2
\]
So the surface area of the original figure is **305.3 in²**.