To find the surface area of a cylinder, we can use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
Given:
- Height \( h = 4 \) yd
- Radius \( r = 7 \) yd
Now, plug the values into the formula:
\[ \text{Surface Area} = 2\pi (7)(4 + 7) \]
Calculate \( 4 + 7 \):
\[ 4 + 7 = 11 \]
Now substitute this back into the formula:
\[ \text{Surface Area} = 2\pi (7)(11) = 2\pi (77) = 154\pi \]
Now, approximate \( \pi \) as 3.14159 and calculate \( 154\pi \):
\[ 154\pi \approx 154 \times 3.14159 \approx 484. indeed \]
Now rounding this to the nearest thousandth:
\[ \text{Surface Area} \approx 484.000 \]
Thus, the surface area of the cylinder is approximately:
\[ \boxed{484.000} , \text{yd}^2 \]