We are given a circle with center O and radius 4 cm. The central angle of a sector is 90 degrees. We need to find the area of the shaded region, which is the sector. The answer must be in terms of $\pi$ and include the correct unit.

1. Problem Description

We are given a circle with center O and radius 4 cm. The central angle of a sector is 90 degrees. We need to find the area of the shaded region, which is the sector. The answer must be in terms of $\pi$ and include the correct unit.

2. Solution Steps

The area of a circle is given by the formula:

$Area = \pi r^2$

where $r$ is the radius of the circle.

The area of a sector with central angle $\theta$ (in degrees) is given by the formula:

$Area_{sector} = \frac{\theta}{360} \pi r^2$

In this problem, the radius $r = 4$ cm and the central angle $\theta = 90$ degrees. Substituting these values into the formula for the area of a sector:

$Area_{sector} = \frac{90}{360} \pi (4)^2$

$Area_{sector} = \frac{1}{4} \pi (16)$

$Area_{sector} = 4\pi$

Since the radius is given in cm, the area will be in $cm^2$. Therefore the area of the shaded region is $4\pi$ $cm^2$.

3. Final Answer

$4\pi \text{ } cm^2$