Answer:
Explanation:
We can start by finding the ratio of the areas of the smaller circle and the larger circle. Let the radius of the smaller circle be r and the radius of the larger circle be R. Then, the area of the smaller circle is πr^2 and the area of the larger circle is πR^2.Since the shaded part is 2/7 of the area of the smaller circle, the unshaded part of the smaller circle is 5/7 of its area. Therefore, the area of the unshaded part of the smaller circle is (5/7)πr^2.Now, let's look at the shaded part of the larger circle. Since the shaded part of the smaller circle is entirely contained within the larger circle, the shaded part of the larger circle is simply the difference between the area of the larger circle and the area of the smaller circle. Therefore, the shaded part of the larger circle is πR^2 - πr^2.We know that the shaded part of the larger circle is equal to 2/7 of the area of the smaller circle, so we can write:πR^2 - πr^2 = (2/7)πr^2Simplifying this equation, we get:πR^2 = (9/7)πr^2Taking the square root of both sides, we get:R = (3/√7)rNow we can find the area of the unshaded part of the larger circle. The area of the entire larger circle is πR^2, so the area of the shaded part is (2/7)πr^2 and the area of the unshaded part is:πR^2 - (2/7)πr^2 = π((3/√7)r)^2 - (2/7)πr^2= π(9/7)r^2 - (2/7)πr^2= (5/7)πr^2Therefore, the total area of the unshaded parts is:(5/7)πr^2 + (5/7)πr^2= (10/7)πr^2So the answer is (10/7)πr^2.