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?
a.1, 831.8in.^2
b. 305.3 in.^2
c. 395, 668.8 in.^2
d. 915.9 in.^2
a.1, 831.8in.^2
b. 305.3 in.^2
c. 395, 668.8 in.^2
d. 915.9 in.^2
Answers
GPT-4o mini
When a figure is dilated by a scale factor \( k \), the relationship between the surface areas of the original figure and the dilated figure can be described as follows:
\[
\text{Surface Area of Dilated Figure} = k^2 \times \text{Surface Area of Original Figure}
\]
In this case, the scale factor \( k \) is 6, so \( k^2 = 6^2 = 36 \).
Let \( A \) be the surface area of the original figure. Then we can express the surface area of the dilated figure, which is given as 10,990.8 in², using the formula:
\[
10,990.8 = 36A
\]
To find \( A \), we can rearrange the equation:
\[
A = \frac{10,990.8}{36}
\]
Now, we can calculate \( A \):
\[
A = 305.3 \text{ in}^2
\]
Thus, the surface area of the original figure is **305.3 in²**.
The correct answer is: **b. 305.3 in²**.
\[
\text{Surface Area of Dilated Figure} = k^2 \times \text{Surface Area of Original Figure}
\]
In this case, the scale factor \( k \) is 6, so \( k^2 = 6^2 = 36 \).
Let \( A \) be the surface area of the original figure. Then we can express the surface area of the dilated figure, which is given as 10,990.8 in², using the formula:
\[
10,990.8 = 36A
\]
To find \( A \), we can rearrange the equation:
\[
A = \frac{10,990.8}{36}
\]
Now, we can calculate \( A \):
\[
A = 305.3 \text{ in}^2
\]
Thus, the surface area of the original figure is **305.3 in²**.
The correct answer is: **b. 305.3 in²**.