To find the surface area of a cylinder, we use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
Where:
- \( r \) is the radius
- \( h \) is the height
- \( \pi \) is approximately 3.14
Given:
- Height \( h = 8 \) yards
- Radius \( r = 7 \) yards
Let's substitute the values into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 7 \times (8 + 7) \]
Now, calculate \( (8 + 7) \):
\[ 8 + 7 = 15 \]
Next, substitute this back into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 7 \times 15 \]
Calculate \( 2 \times 3.14 = 6.28 \):
\[ \text{Surface Area} = 6.28 \times 7 \times 15 \]
Now \( 7 \times 15 = 105 \):
\[ \text{Surface Area} = 6.28 \times 105 \]
Finally, compute \( 6.28 \times 105 \):
\[ \text{Surface Area} = 659.4 \text{ square yards} \]
None of the options provided (252.77, 329.7, 577.76, or 252.77 square yards) matches the calculated surface area.
Since the options provided do not include the correct answer, it appears there may have been an error in either the problem statement or potential answer choices. However, using the calculations shown, the correct surface area of the cylinder with the given dimensions is 659.4 square yards.