Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Write an expression for the area of the shaded region in its simplest form. Show all of your steps.
To find the area of the shaded region, we need to subtract the area of the smaller circle from the area of the larger circle.
Let's assume the radius of the larger circle is R and the radius of the smaller circle is r.
The formula for the area of a circle is A = πr^2.
Therefore, the area of the larger circle is A_larger = πR^2.
Similarly, the area of the smaller circle is A_smaller = πr^2.
To find the area of the shaded region, we subtract the area of the smaller circle from the area of the larger circle: A_shaded = A_larger - A_smaller.
In terms of the radius, this becomes:
A_shaded = πR^2 - πr^2.
To simplify further, we can factor out π:
A_shaded = π(R^2 - r^2).
Therefore, the expression for the area of the shaded region is A_shaded = π(R^2 - r^2).