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

First, we need to calculate the radius of the cylinder. The radius is half of the diameter, so the radius is 12cm / 2 = 6cm.

The formula for the surface area of a cylinder is 2πr(r + h), where r is the radius and h is the height.

Plugging in the values, we get:
Surface area = 2π(6)(6 + 30)
Surface area = 2π(6)(36)
Surface area = 2π(216)
Surface area = 432π

Therefore, the area of the cylinder is 432π square centimeters.

The area of a cylinder is given by the formula:

```
A = 2πrh + 2πr²
```

Where:

- A is the area of the cylinder
- r is the radius of the cylinder
- h is the height of the cylinder

In this case, the diameter of the cylinder is 12 cm, which means the radius is 6 cm. The height of the cylinder is 30 cm. Substituting these values into the formula, we get:

```
A = 2π(6 cm)(30 cm) + 2π(6 cm)²
A = 360π cm² + 72π cm²
A = 432π cm²
```

Therefore, the area of the cylinder is 432π cm².