https://file.aiquickdraw.com/mathbot/file/1730138332098jay9mg15.jpg

To find the surface area of a cylinder, we use the formula:

\[
\text{Surface Area} = 2\pi r (r + h)
\]

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

From the image:
- The diameter is \( 8 \, \text{cm} \), so the radius \( r = \frac{8}{2} = 4 \, \text{cm} \).
- The height \( h = 15 \, \text{cm} \).

### Calculations:
1. Substitute \( r = 4 \) and \( h = 15 \) into the formula:
   \[
   \text{Surface Area} = 2 \pi \cdot 4 \cdot (4 + 15)
   \]

2. Simplify inside the parentheses:
   \[
   \text{Surface Area} = 2 \pi \cdot 4 \cdot 19
   \]

3. Multiply \( 4 \) and \( 19 \):
   \[
   \text{Surface Area} = 2 \pi \cdot 76
   \]

4. Multiply \( 2 \) and \( 76 \):
   \[
   \text{Surface Area} = 152 \pi
   \]

5. Using \( \pi \approx 3.14159 \):
   \[
   \text{Surface Area} \approx 152 \times 3.14159 = 477.52 \, \text{cm}^2
   \]

### Final Answer:
The surface area of the cylinder is approximately \( 477.52 \, \text{cm}^2 \) (rounded to two decimal places).

Would you like further explanation on any part of this solution?

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Here are some related questions:
1. How do you calculate the volume of a cylinder with similar dimensions?
2. How would the surface area change if the radius were doubled?
3. What is the lateral (side) surface area of a cylinder and how is it calculated?
4. How does the surface area of a cylinder compare to that of a sphere with the same radius?
5. How would the surface area formula change if the cylinder were hollow?

**Tip:** Always verify units and ensure they match in geometry problems for accurate calculations.

Find the surface area of the cylinder. Give your answer to two decimal places. Diameter = 8 cm, Height = 15 cm.

Learn how to find the surface area of a cylinder with a diameter of 8 cm and a height of 15 cm. This solution covers the surface area formula for cylinders, providing a detailed step-by-step guide suitable for students in Grades 6-8.

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