Cant understand this math problem

Test Preparation SAT Preparation
1

<ol>
<li>Semicircular arcs AB,AC,BD,CD divide the circle above into regions. The points show along the diameter AD divide it into 6 equal parts. If AD=6, what is the total area of the shaded regions?
a.4pi
b.5pi
c.6pi
d.12pi
e.24pi</li>
</ol>

<p>[url=<a href="http://tinypic.com/view.php?pic=25tiwib&s=7%5DImage"&gt;http://tinypic.com/view.php?pic=25tiwib&s=7]Image&lt;/a> - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting<a href="someone%20else's%20link...I%20found%20it...">/url</a></p>

<p>How do i do this problem? I've looked on Google, but I haven't found a good through explanation. So, can someone please give me a very good explanation as to how you got the right answer?</p>

<p>Thanks in advance</p>

2

<p>200 views, and no one knows. Could someone please explain?</p>

3

<p>Could you post a better picture…?</p>

4

<p>Nevermind. Is the answer c?</p>

5

<p>This is a question from the Blue Book. Test 3, Section 2, Question 17 on page 518.</p>

<p>Here’s two ways to solve it:

  1. AD = 6 = diameter. Therefore the radius is 3. Therefore area of the whole circle is 9pi. Cross out answer choices D and E.</p>

<ol>
<li><p>Eyeballing the top 1/2 of the circle. The unshaded region is less than 1/2 of the shaded region. Therefore the answer is greater than 1/2 the area - 4.5 pi. Throw out answer choice A. </p></li>
<li><p>The unshaded region is definitely closer to 1/4 than 1/2 of the shaded region, so the answer should be closer to 6pi than 5pi. Therefore choose choice C.</p></li>
</ol>

<p>Here’s the mathy way to solve it:

  1. Area of whole circle is 9pi</p>

<p>2.Just look at the top 1/2 of the circle. The shaded area is arc AD - arc AC then we need to add back in arc AB. </p>

<ol>
<li><p>Area of arc AD is 4.5pi (just 1/2 of the whole circle) Area of of arc AC - diameter is 4, therefore radius is 2, therefore area is 1/2 pi 2^2, which is 2pi. Area of arc AB - diameter is 2, therefore radius is 1, therefore area is 1/2 pi1^2 which is 1/2 pi.</p></li>
<li><p>So 4.5 pi - 2 pi + .5 pi = 3 pi. But this is just for the top 1/2 of the circle. So multiply it by 2 to get the shaded area of the whole circle 3 pi x 2 = 6pi. Answer C.</p></li>
</ol>

6

<p>Try rotating the bottom half 180deg around its vertical axis - you’ll see three complete circles.</p>

7

<p>Okay, found a couple of minutes to draw what I suggested.

<a href=“http://i44.■■■■■■■.com/15cf5fm.jpg[/IMG]”>http://i44.■■■■■■■.com/15cf5fm.jpg

</a>
The smallest diameter is 2, the medium - 4, the largest - 6.
The total area of the shaded regions:
pi 1^2 + (pi 3^2 - pi 2^2) = 6 pi</p>