The surface area \( S \) of a cylinder is given by the formula:
\[ S = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given that the diameter of the cylinder is 2 yards, we can find the radius:
\[ r = \frac{\text{diameter}}{2} = \frac{2 \text{ yards}}{2} = 1 \text{ yard} \]
The height \( h \) is given as 3 yards.
Now, we can substitute these values into the surface area formula. Using \( \pi \approx 3.14 \):
- Calculate \( 2\pi r^2 \):
\[ 2\pi r^2 = 2 \times 3.14 \times (1)^2 = 2 \times 3.14 \times 1 = 6.28 \]
- Calculate \( 2\pi rh \):
\[ 2\pi rh = 2 \times 3.14 \times 1 \times 3 = 2 \times 3.14 \times 3 = 18.84 \]
- Now, add both parts together to get the total surface area:
\[ S = 6.28 + 18.84 = 25.12 \]
Thus, the surface area of the cylinder is \( \boxed{25.12} \) square yards.