Dividing an annulus
Geometry
Level
pending
You have an annulus with an outer radius of 7 m and an inner radius of 1 m.
You need to draw a third circle to split it into two annuluses of equal area. How large, in m, should the radius of your dividing circle be? Figure your solution to 3 decimal places.
The answer is 5.000.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Your annulus has an area of (49 - 1) = 48 * pi square meters. So you need to split it into two annuluses that each have an area of 48/2 = 24 * pi square meters.
The hole in the center has an area of 1 * pi square meters, so your dividing circle has to enclose an area of (24 + 1) = 25 * pi square meters.Since for a circle, A = pi * (radius) squared, your radius has to be the positive square root of 25, which is exactly 5 meters.