What is the area of a cylinder with a diameter of 12 cm and heights of 30 cm. What is the equation

To calculate the area of a cylinder, we typically need to find the **surface area**, which consists of two parts:

1. The area of the two circular bases.
2. The area of the curved (lateral) surface.

The formula for the **total surface area (A)** of a cylinder is:

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

Where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.1416.

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

### Step-by-step calculation:

1. **Area of the two bases:**
   \[
   2\pi r^2 = 2\pi (6)^2 = 2\pi (36) = 72\pi \, \text{cm}^2
   \]
   
2. **Lateral surface area:**
   \[
   2\pi rh = 2\pi (6)(30) = 360\pi \, \text{cm}^2
   \]

3. **Total surface area:**
   \[
   A = 72\pi + 360\pi = 432\pi \, \text{cm}^2
   \]
   Now, substituting \( \pi \approx 3.1416 \):
   \[
   A \approx 432 \times 3.1416 \approx 1357.17 \, \text{cm}^2
   \]

### Final Answer:
The total surface area of the cylinder is approximately **1357.17 cm²**.

Would you like more details on any step?

Here are 5 related questions:
1. How would the surface area change if the height were doubled?
2. What would be the lateral surface area if the height was halved?
3. How does changing the diameter affect the total surface area?
4. Can you calculate the volume of the cylinder using a similar method?
5. What is the difference between lateral and total surface area?

**Tip:** Always ensure to double-check whether the problem asks for the lateral surface area or the total surface area of a cylinder.

What is the area of a cylinder with a diameter of 12 cm and height of 30 cm? What is the equation?

Learn how to calculate the total surface area of a cylinder with a 12 cm diameter and a 30 cm height. This solution breaks down geometry concepts and key formulas to help students understand cylindrical surface area calculations. Ideal for Grades 8-10.

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