Circle A is in the interior of circle B. The diameter of circle B is 16 cm. What is the diameter of circle A for which the ratio of the shaded area to the area of circle A is 8:1?
+128407 Note that we could move A to B and have concentric circles
The radius of the larger circle = 8
We are looking for this
Area of circle B - area of circle A = shaded area
And
Shaded area = 8 * area of circle A....so
Area of circle B - area of circle A = 8 * area ofcircle A
Area of circle B = 9 * area of circle A
pi * 8^2 = 9 *pi * r^2 where r is the radius of circle A
64 = 9 r^2
64/9 = r^2 take the positive root of both sides
8 / 3 cm = r = radius of smaller circle A
So....the diameter of circle A = 2 (8/3) = 16 / 3 cm
+1694 Circle B area = 64pi
Circle A area = (64pi) / 9
Circle A radius = sqrt(64 / 9)
Circle A diameter = 2[sqrt(64 / 9)]
D = 5 1/3 cm
