How do you calculate the area of an annulus?

To find the area of an annulus, which is the region between two concentric circles (a larger circle of radius R and a smaller circle of radius r), you need to calculate the difference in the areas of these two circles. The area of a circle is given by the formula A = πR², where R is the radius of the circle.

For the larger circle with radius R, the area is πR², and for the smaller circle with radius r, the area is πr². To find the area of the annulus, you subtract the area of the smaller circle from the area of the larger circle. This gives you:

Area of annulus = Area of larger circle - Area of smaller circle

= πR² - πr²

This derivation confirms that option A is correct, as it accurately represents the area of the annulus by taking the difference between the two circle areas.