Calculate the area of a cylinder with a diameter of 12cm and height of 30cm

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

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

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

Given:
- Diameter = 12 cm, so the radius \( r = \frac{12}{2} = 6 \) cm,
- Height \( h = 30 \) cm.

Now, we can plug these values into the formula.

1. **Calculate the area of the two circular bases**:

\[
2\pi r^2 = 2\pi (6)^2 = 2\pi \times 36 = 72\pi \text{ cm}^2
\]

2. **Calculate the lateral surface area**:

\[
2\pi r h = 2\pi \times 6 \times 30 = 360\pi \text{ cm}^2
\]

3. **Total surface area**:

\[
A = 72\pi + 360\pi = 432\pi \text{ cm}^2
\]

Approximating \( \pi \approx 3.1416 \):

\[
A = 432 \times 3.1416 \approx 1357.17 \text{ cm}^2
\]

So, the surface area of the cylinder is approximately **1357.17 cm²**.

Would you like more details on any part of the calculation?

Here are some related questions for you:
1. How do you calculate the volume of a cylinder?
2. What is the surface area formula for a cone?
3. How does the surface area change if the height is doubled but the radius remains constant?
4. What happens to the surface area if the diameter is halved?
5. Can you derive the surface area formula for a cylinder from basic geometric principles?

**Tip:** When calculating the surface area of a cylinder, remember to include both the lateral surface area and the area of the two circular bases!

Calculate the area of a cylinder with a diameter of 12cm and height of 30cm.

Learn how to calculate the surface area of a cylinder with a diameter of 12 cm and a height of 30 cm. This step-by-step solution covers geometry concepts, including the surface area formula for cylinders and the calculation of both the circular base and lateral surface areas. Suitable for students in Grades 6-8.

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