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:
\[ \text{Surface Area of Dilated Figure} = k^2 \times \text{Surface Area of Original Figure} \]
In this case, the scale factor \( k \) is 6, and the surface area of the dilated figure is 10,990.8 in². We can set up the equation as follows:
\[ 10,990.8 = 6^2 \times \text{Surface Area of Original Figure} \]
Calculating \( 6^2 \):
\[ 6^2 = 36 \]
Now we can rewrite the equation:
\[ 10,990.8 = 36 \times \text{Surface Area of Original Figure} \]
Now, we solve for the Surface Area of the Original Figure:
\[ \text{Surface Area of Original Figure} = \frac{10,990.8}{36} \]
Calculating that gives:
\[ \text{Surface Area of Original Figure} = 305.3 \text{ in}^2 \]
Therefore, the surface area of the original figure is \( 305.3 \text{ in}^2 \), which corresponds to option:
c. 305.3 in²