Question 1182220

The 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. 
<pre>Area of larger circle: {{{matrix(1,5, pi*r^2, "=", pi(12)^2, "=", 144pi)}}}
With radius of smaller circle being r, we get the area of the smaller circle as: {{{pi*r^2}}}
Area of shaded region: {{{144*pi - pi*r^2}}}
Area of shaded region is also {{{1/3}}} the area of the larger circle.
We then get: {{{matrix(1,3, (1/3) * 144pi, "=", 144*pi - pi*r^2)}}}
           {{{matrix(5,3, 48pi, "=", 144*pi - pi*r^2, 48pi - 144pi, "=", - pi*r^2, - 96pi, "=", - pi*r^2, (- 96pi)/(- pi), "=", r^2, 96, "=", r^2)}}}
                     {{{matrix(3,3, r, "=", " "+- sqrt(96), r, "=", " "+- sqrt(16 * 6), r, "=", " "+- 4sqrt(6))}}}
Since this is a measurement, CORRECT answer is {{{highlight_green(4sqrt(6))}}}, as the negative value for the radius is IGNORED.