The problem asks for the area of the shaded region of a circle. The circle has a radius of 4 cm, and the central angle of the unshaded sector is 90 degrees. We need to give the answer in terms of $\pi$.

1. Problem Description

The problem asks for the area of the shaded region of a circle. The circle has a radius of 4 cm, and the central angle of the unshaded sector is 90 degrees. We need to give the answer in terms of $\pi$.

2. Solution Steps

First, find the area of the entire circle. The formula for the area of a circle is:

$A = \pi r^2$

where $r$ is the radius of the circle. In this case, $r = 4$ cm.

$A = \pi (4)^2 = 16\pi$ cm$^2$

Next, we need to find the area of the unshaded sector. The central angle of the sector is 90 degrees. Since a full circle is 360 degrees, the sector is $\frac{90}{360} = \frac{1}{4}$ of the entire circle.

So, the area of the unshaded sector is:

$A_{sector} = \frac{1}{4} \times 16\pi = 4\pi$ cm$^2$

To find the area of the shaded region, subtract the area of the unshaded sector from the area of the entire circle:

$A_{shaded} = A - A_{sector} = 16\pi - 4\pi = 12\pi$ cm$^2$

3. Final Answer

The area of the shaded region is $12\pi$ cm$^2$.