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To find the surface area of the cylinder with a base radius of 4 cm and a height of 9 cm, we can use the formula for the total surface area of a cylinder:

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

Where:
- \( r = 4 \) cm (radius),
- \( h = 9 \) cm (height),
- \( \pi = 3.14 \) (as given in the problem).

Let's break it down into two parts:

1. **Area of the two circular bases**:
\[
2\pi r^2 = 2 \times 3.14 \times (4)^2 = 2 \times 3.14 \times 16 = 100.48 \, \text{cm}^2
\]

2. **Area of the lateral surface**:
\[
2\pi r h = 2 \times 3.14 \times 4 \times 9 = 2 \times 3.14 \times 36 = 226.08 \, \text{cm}^2
\]

Now, sum the two areas to get the total surface area:

\[
A = 100.48 \, \text{cm}^2 + 226.08 \, \text{cm}^2 = 326.56 \, \text{cm}^2
\]

Thus, the surface area of the cylinder is **326.56 cm²**.

Would you like more details, or have any questions?

Here are 5 related questions:
1. How would the surface area change if the radius was doubled?
2. How do you calculate the volume of this cylinder?
3. What happens to the surface area if the height is reduced by half?
4. What is the relationship between lateral surface area and the height of a cylinder?
5. How would the surface area change if the value of \( \pi \) was more precise, like \( \pi \approx 3.1416 \)?

**Tip:** When dealing with surface area of cylinders, remember that the lateral surface area is just a rectangle wrapped around the cylinder!

Find the surface area of a cylinder with a base radius of 4 cm and a height of 9 cm. Use the value 3.14 for π, and do not do any rounding. Be sure to include the correct unit.

Learn how to find the surface area of a cylinder with a radius of 4 cm and a height of 9 cm using the formula A = 2πr^2 + 2πrh. This guide uses π as 3.14 for simplicity and provides a detailed step-by-step solution. Suitable for students in Grades 6-8.

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