Three circles have the same centre. The radius of the smaller circle is sqrt(3). The area of the region between the larger circle and the one in the middle is equal to the area of the smaller circle, and the area between the one in the middle and the smaller is equal to the area of the smaller circle. What is the radius of the larger circle?
+128473 Area of smaller circle = pi (sqrt (3))^2 = 3pi
Area of middle circle - area of smaller circle = area of smaller circle
Area of middle circle - 3pi = 3pi
Area of middle circle = 6pi
So
The radius of the second circle must be sqrt (6)
And the area of the outer circle -area of middle circle = area of smaller circle
Area of outer circle - 6pi = 3pi
Area of outer circle = 9pi
So....the radius of the outer circle must = sqrt (9) = 3
