Since the radii of the two concentric circles are 3 centimeters and 7 centimeters, the area of the shaded region is 40π square centimeters.
In Mathematics and Euclidean Geometry, the area of a circle can be calculated by using this mathematical equation (formula):
Area of a circle, A = π

Where:
r represents the radius of a circle.
By substituting the given parameters into the formula for the area of a circle, the area of the larger circle is given by;
Area of larger circle = π ×

Area of larger circle = 49π square centimeters.
Area of smaller circle = π ×

Area of smaller circle = 9π square centimeters.
Now, we can determine the area of the shaded region as follows;
Area of the shaded region = Area of larger circle - Area of smaller circle
Area of the shaded region = 49π - 9π
Area of the shaded region = 40π square centimeters.