To find the surface area of a cylinder, we use the formula:
\[ SA = 2\pi r(h + r) \]
where \( r \) is the radius and \( h \) is the height. Given the radius \( r = 2 \) yards and the height \( h = 3 \) yards, we can substitute these values into the formula.
Using \( \pi \approx 3.14 \):
\[ SA = 2 \times 3.14 \times 2(3 + 2) \]
Calculating the values step by step:
- Calculate \( h + r = 3 + 2 = 5 \).
- Calculate the area:
\[ SA = 2 \times 3.14 \times 2 \times 5 \]
\[ SA = 2 \times 3.14 \times 10 \]
\[ SA = 62.8 \]
Now calculate the curved surface area separately:
\[ \text{Curved Surface Area} = 2\pi rh \]
\[ = 2 \times 3.14 \times 2 \times 3 \]
\[ = 2 \times 3.14 \times 6 = 37.68 \]
Calculate the area of the top and bottom:
\[ \text{Area of the top and bottom} = 2\pi r^2 \]
\[ = 2 \times 3.14 \times 2^2 \]
\[ = 2 \times 3.14 \times 4 = 25.12 \]
Finally, add both areas:
\[ SA = 37.68 + 25.12 = 62.8 \]
Thus, the correct calculation leads to the total surface area:
\[ \text{Surface Area} = 62.8 \text{ square yards} \]
Since the available responses don't include 62.8, there may be a miscalculation in the options provided. Based on the calculations, the surface area derived from the dimensions provided is correct.
However, among the responses you have provided, none match the calculated surface area of 62.8 square yards.