A cylinder has a diameter of 6 cm and a height of 3 cm.

What is the surface area of the cylinder?

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

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

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

### Step 1: Find the radius
Since the diameter of the cylinder is given as 6 cm, the radius is half of the diameter:
\[
r = \frac{6}{2} = 3 \, \text{cm}
\]

### Step 2: Plug values into the formula
Now, substitute \( r = 3 \, \text{cm} \) and \( h = 3 \, \text{cm} \) into the surface area formula:

\[
\text{Surface Area} = 2\pi (3^2) + 2\pi (3)(3)
\]

\[
\text{Surface Area} = 2\pi (9) + 2\pi (9)
\]

\[
\text{Surface Area} = 18\pi + 18\pi = 36\pi
\]

### Step 3: Calculate the surface area
Using \( \pi \approx 3.1416 \):

\[
\text{Surface Area} \approx 36 \times 3.1416 = 113.0976 \, \text{cm}^2
\]

### Final Answer:
The surface area of the cylinder is approximately **113.10 cm²**.

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. How would the surface area change if the diameter doubled?
2. What is the volume of this cylinder?
3. How would the surface area formula adjust if the cylinder were hollow?
4. How does the surface area change if the height is halved while keeping the diameter constant?
5. How does the surface area compare between a cylinder and a sphere with the same radius?

**Tip:** In problems involving cylinders, always remember to distinguish between the radius and the diameter—it's a common source of error!

A cylinder has a diameter of 6 cm and a height of 3 cm. What is the surface area of the cylinder?

Learn how to calculate the surface area of a cylinder with a diameter of 6 cm and a height of 3 cm. This step-by-step solution explains the formula for surface area and provides detailed calculations. Ideal for students in Grades 6-8.

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