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To find the total surface area (SA) of a cylinder, we use the following formula:

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

Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder, and
- \( \pi \approx 3.14 \) (as given in the problem).

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

Now we can calculate the surface area step by step.

### Step 1: Calculate the area of the two circular bases
\[
2\pi r^2 = 2 \times 3.14 \times (4)^2 = 2 \times 3.14 \times 16 = 100.48 \, \text{cm}^2
\]

### Step 2: Calculate the lateral surface area
\[
2\pi r h = 2 \times 3.14 \times 4 \times 15 = 2 \times 3.14 \times 60 = 376.8 \, \text{cm}^2
\]

### Step 3: Add the areas together
\[
\text{Total Surface Area} = 100.48 + 376.8 = 477.28 \, \text{cm}^2
\]

Thus, the total surface area of the cylinder is approximately **477.28 cm²**, rounded to the nearest hundredth.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the volume of the same cylinder?
2. How would the surface area change if the height were doubled?
3. How is the lateral surface area affected by increasing the radius?
4. Can you find the surface area if only the lateral part of the cylinder was required?
5. What is the effect of using an exact value of \( \pi \) (3.14159) instead of 3.14?

**Tip:** Always double-check units and make sure all measurements are consistent throughout the problem.

Find the total surface area of the cylinder with a radius of 4 cm and height of 15 cm, using π ≈ 3.14.

Learn how to find the total surface area of a cylinder with a radius of 4 cm and height of 15 cm. This problem uses the formula for the surface area of a cylinder, and includes step-by-step calculations. Suitable for students in Grades 7-9.

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