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The image provides a problem about finding the surface area of a cylinder. The formula for the surface area \( A \) of a cylinder is:

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

where:
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \approx 3.14 \).

From the image:
- Radius \( r = 2 \, \text{yd} \),
- Height \( h = 3 \, \text{yd} \).

### Step-by-step calculation:
1. **Calculate the area of the two circular bases** (since there are two):
   \[
   2\pi r^2 = 2 \times 3.14 \times (2)^2 = 2 \times 3.14 \times 4 = 25.12 \, \text{yd}^2
   \]

2. **Calculate the lateral surface area** (the side of the cylinder):
   \[
   2\pi rh = 2 \times 3.14 \times 2 \times 3 = 2 \times 3.14 \times 6 = 37.68 \, \text{yd}^2
   \]

3. **Add the two areas together** to get the total surface area:
   \[
   A = 25.12 + 37.68 = 62.8 \, \text{yd}^2
   \]

So, the surface area of the cylinder is **62.8 yd²**.

Would you like any further details or have any questions?

Here are five related questions:
1. What is the formula for the volume of a cylinder?
2. How does changing the height affect the surface area?
3. What happens to the surface area if the radius is doubled?
4. Can you derive the formula for the surface area of a cylinder?
5. How is the lateral surface area of a cylinder related to the circumference of the base?

**Tip:** Always remember to account for both the lateral surface area and the two circular bases when calculating the surface area of a cylinder.

The surface area of a cylinder = 2πr² + 2πrh. Use 3.14 for π. What is the surface area of this cylinder? Radius = 2 yd, Height = 3 yd.

Learn how to calculate the surface area of a cylinder with radius 2 yd and height 3 yd using the formula 2πr² + 2πrh. Includes a detailed step-by-step solution, showing how to compute the area of the two circular bases and the lateral surface area.

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