In the diagram above are two concentric circles of radii r and R respectively with center O. If r = 2/3R, express the area of the shaded portion in terms of...

In the diagram above are two concentric circles of radii r and R respectively with center O. If r = 2/3R, express the area of the shaded portion in terms of π and R

Answer Details

The area of the shaded region is equal to the difference between the areas of the two circles. The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. Let's find the radius of the smaller circle: r = 2/3R Now we can express the area of the shaded region in terms of π and R: Area of shaded region = Area of larger circle - Area of smaller circle A = πR^2 - π(2/3R)^2 A = πR^2 - 4/9πR^2 A = (9/9πR^2 - 4/9πR^2) A = 5/9πR^2 Therefore, the answer is 5/9πR^2.