Question 909337

Diagram of circle with outer edge shaded.  The outer circle has diameter 8 inches. The area of the shaded ring is equal to the are of the inner, non-shaded circle. What is the radius of the inner circle? Express your answer as a decimal to the nearest tenth.
<pre>
Let radius of smaller, non-shaded, inner circle, be r
Then area of smaller, non-shaded circle is: {{{pi*r^2}}}
Now, since the area of the smaller, non-shaded circle and the shaded area are equal, then
the area of the smaller, non-shaded circle and the shaded region = {{{2(pi*r^2)}}}, or {{{2pi*r^2}}}
Area of larger circle is: {{{pi*4^2}}}, or {{{16pi}}}
Therefore, we get: {{{2pi*r^2 = 16pi}}}
{{{2pi*(r^2) = 2pi*(8)}}} ------ Factoring out GCF, {{{2pi}}}
{{{r^2 = 8}}}  
r, or radius of smaller, non-shaded, inner circle = {{{sqrt(8)}}}, or {{{2sqrt(2)}}}, or {{{2.828427125}}} &#8776; {{{highlight_green(2.8)}}} inches