To find the surface area of a cylinder, we can use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius,
- \( h \) is the height.
Given:
- The width of the cylinder is 2 yards, so the radius \( r \) is half of the width: \[ r = \frac{2}{2} = 1 \text{ yard} \]
- The height \( h \) is 3 yards.
Now, plug the values into the formula using \( \pi \approx 3.14 \):
-
Calculate the area of the two circular bases: \[ 2\pi r^2 = 2 \times 3.14 \times (1)^2 = 2 \times 3.14 \times 1 = 6.28 \text{ square yards} \]
-
Calculate the lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times (1) \times (3) = 2 \times 3.14 \times 3 = 18.84 \text{ square yards} \]
-
Add both areas to find the total surface area: \[ \text{Surface Area} = 6.28 + 18.84 = 25.12 \text{ square yards} \]
Therefore, the surface area of the cylinder is 25.12 square yards.