A paint roller is a cylinder that is 15 cm long with a radius of three centimeters. Find the area of the wall it can cover in one revolution.

The formula for the surface area of a cylinder is given by:

Surface Area = 2πr(r + h)

Where r is the radius and h is the height of the cylinder.

Given that the radius of the paint roller is 3 cm and the height is 15 cm, we can plug these values into the formula:

Surface Area = 2π(3)(3 + 15)
Surface Area = 2π(3)(18)
Surface Area = 2π(54)
Surface Area = 108π

Therefore, the area of the wall that the paint roller can cover in one revolution is 108π square centimeters.

The surface area of a cylinder is given by the formula:

```
A = 2πrh + 2πr²
```

where:

- A is the surface area
- r is the radius
- h is the height

In this case, the radius is 3 cm and the height is 15 cm. So, the surface area is:

```
A = 2π(3 cm)(15 cm) + 2π(3 cm)²
= 90π cm² + 18π cm²
= 108π cm²
```

Therefore, the paint roller can cover an area of 108π cm² in one revolution.