<p>Visual: circle with a piece (like a piece of pie) shaded in</p>
<p>Length of minor arc AB is pi/2 and the area of the shaded region is 1/6 the area of the entire circle. What is the radius of a circle that is 1/2 the area of the above circle? </p>
<p>How do you find the radius of the given circle to take half of it?</p>
<p>Gracias!</p>
<p>I think this is how you do it....</p>
<p>So you know that the shaded region is 1/6 of the entire area. That means that arc AB is 1/6 of the entire circle's circumference. So pi/2 = 1/6C. Therefore, the circumference is 3 pi. C = 2<em>pi</em>r, so radius = 3/2. Area then = 2.25 pi. 1/2 of that = 1.125 pi. 1.125 is the same as 9/8....9/9 pi = pi*r^2....r = the square root of (9/8). In decimal form that is 1.06066ish. In fraction form that is: (3) / (sqt8)....or 3 / 2sqt2. </p>
<p>Hopefully one of those is the answer...if not, then I definitaly don't deserve my math score. Also, you mentioned taking half of the radius of the given circle....that wouldn't work because the area of a circle involves "radius^2". You would have to take half of the area, then from that find the radius. Hope this was right or at least somewhat helpful.</p>
<p>Yeah it was the exact same anwser as the book! (so you DEFINITELY deserve your math score! lol) </p>
<p>thanks SO much!!</p>