Question 146706
It always helps to draw a picture



note: "R" is the radius of the larger circle and "r" is radius of the smaller circle. Also, I divided the chord in half. 




<a href="http://www.flickr.com/photos/7963298@N08/2617453180/" title="circle by jim_thompson5910, on Flickr"><img src="http://farm4.static.flickr.com/3120/2617453180_844ea2e243.jpg" width="487" height="471" alt="circle" /></a>



From the picture, we can see that the radius R is the hypotenuse of the triangle with legs of "r" and 4. So this means


{{{4^2+r^2=R^2}}}



{{{16+r^2=R^2}}} Square 4 to get 16



{{{16=R^2-r^2}}} Subtract {{{r^2}}} from both sides



So {{{R^2-r^2=16}}}


Now the area of the larger circle is {{{A=pi*R^2}}} and the area of the smaller circle is {{{A=pi*r^2}}}



Since we want the area between the two circles, we must subtract the two areas to get: {{{pi*R^2-pi*r^2}}}



{{{pi(R^2-r^2)}}} Factor out the GCF {{{pi}}}



{{{pi(16)}}} Plug in {{{R^2-r^2=16}}}. In other words, replace {{{R^2-r^2}}} with 16



{{{16pi}}} Rearrange the terms



So the area between the two circles is {{{16pi}}}