Question 1182220
he area of the shaded region represents one-third of the total, What is the size of the radii such that this is possible? 

The radius of the whole circle is 12cm while the shaded region is a ring in the middle with a small not shaded circle in the middle. 
;
Find 1/3 of the area of the whole circle
{{{1/3}}}*{{{pi*12^2 = 150.796}}}
let R = radius to the outer ring 
let r = radius to the inner ring 
:
{{{(pi*R^2) - (pi*r^2) = 150.796}}}
{{{pi(R^2 - r^2) = 150.796}}}
divide both sides by pi
{{{R^2 - r^2 = 48}}}
graph this equation
{{{R = sqrt(48+r^2)}}} Where R is on the y axis, r is on the x axis
first integer solution
R = 8, r = 4
see if that works
{{{(pi*8^2) - (pi*4^2)}}}
201.062 - 50.265 = 150.797 
The radii of 8 and 4 make this possible