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To solve this problem, we need to calculate the surface area of a cylinder, which consists of two parts:

1. The **area of the two circular bases**.
2. The **area of the curved side (lateral surface area)**.

The formula for the total surface area of a cylinder is given by:

\[
A = 2\pi r^2 + 2\pi rh
\]

Where:
- \(r\) is the radius of the cylinder's base.
- \(h\) is the height of the cylinder.

### Given:
- Diameter of the base = 4 yards, so the radius \(r = \frac{4}{2} = 2\) yards.
- Height \(h = 3\) yards.

Now, plug the values into the formula.

1. **Area of the two circular bases**:
   \[
   2\pi r^2 = 2\pi (2)^2 = 2\pi \times 4 = 8\pi \, \text{square yards}.
   \]

2. **Area of the lateral surface**:
   \[
   2\pi rh = 2\pi \times 2 \times 3 = 12\pi \, \text{square yards}.
   \]

Finally, the **total surface area** is:
\[
A = 8\pi + 12\pi = 20\pi \, \text{square yards}.
\]

Thus, the surface area of the cylinder is \( \mathbf{20\pi} \, \text{square yards} \).

Would you like further clarification on this solution?

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### Related Questions:
1. How do you calculate the surface area of a cone with a given height and radius?
2. What is the formula for the volume of a cylinder, and how would you compute it for the same cylinder?
3. How would the surface area change if the cylinder's height were doubled?
4. What is the relationship between the surface area and volume of a cylinder?
5. How does the surface area formula differ for an open-top cylinder?

**Tip:** Always ensure that you use the correct unit for your final answer to avoid confusion, especially in geometry problems.

Find the surface area of a cylinder with a base diameter of 4 yards and a height of 3 yards. Write your answer in terms of π, and be sure to include the correct unit.

Learn how to calculate the surface area of a cylinder with a base diameter of 4 yards and a height of 3 yards. This problem demonstrates how to apply the formula for the surface area of a cylinder, including both the circular base and lateral surface areas, using π in the answer. Suitable for students in Grades 6-8.

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