Can anyone help me with this problem, it seems to be impossible.

Test Preparation SAT Preparation
1

<p><a href="http://img684.imageshack.us/img684/1897/sat.jpg%5B/url%5D"&gt;http://img684.imageshack.us/img684/1897/sat.jpg&lt;/a>
That is the diagram
The two semicircles in the figure have centers R and S, if RS= 12, what is the total length of the curve?</p>

<p>I keep trying to use circumference to find the length of the arc, but all that is doing is adding pi into the equation, the answers for multiple choice are 8,9,12,15,or 16</p>

<p>Thank you very much.
The Question is from the Official Practice Exam 2009-2010 from CollegeBoard.</p>

2

<p>are you sure thats the answer? i got 12π</p>

<p>EDIT- i did it by seeing 12 was distance between each so the radius of each is 6, circumference is 2πr so i did that with 6, twice and divided by two because theyre only half circles…</p>

3

<p>The Answer was 12, just 12, should one discard the radians?</p>

4

<p>I must have done it wrong… eek good thing i didnt get this on my SAT hehe, i now await the correct answer with you lmao</p>

5

<p>Anyone know how to do it?</p>

6

<p>Can you post which page and what problem number this is? I feel like there’s a missing piece of info in the problem.</p>

7

<p>Page 44, Problem 5 in Section 9</p>

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<p>You guys are right, the answer is 12pi. The MC answers have pi’s in them. But you have to be careful about assuming that the radius of each circle is 6 (post #2) because one of the semicircles in the figure is smaller than the other. Assuming that r is 6 works for this problem but it may not work in another problem like this. So we know the radius of both circles combined is 12. We plug that into the C=2rpi and get 24pi for the circumference of both. Since both are semicircles we divide that into 2 to get 12pi.</p>

9

<p>the answer is indeed 12pi. The circles are not equal in radius but that doesn’t matter. For example if one circle had radius 4 and the other 8:</p>

<p>half circle 1 (r=4)
2pi*4 = 8pi
8pi/2(because it’s a half circle) = 4pi</p>

<p>half circle 2 (r=8)
2pi*8 = 16pi
16pi/2 = 8pi</p>

<p>4pi+8pi = 12pi = length of both arcs added.</p>

<p>now if the radii were 1 and 11 or 6 and 6 or 3 and 9, the answer would not differ which should leave you happy with picking 12.</p>

10

<p>THERE WAS A MISTAKE WITH THIS QUESTION! CB messed up! I got a little card in my booklet saying this book has a mistake Section 9, question 5 the answer choices should be changed to
8pi
9pi
12pi
15pi
and 16pi from there you could obviously tell it is 5 pi</p>

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<p>we already know there was a mistake, only the pi’s are missing. That doesn’t mean that you should get the question wrong or omit it. You should know the answer is 12.</p>

12

<p>I was just statingthe fact that cb admitted to this mistake it tends to trip someone up since less then 1% of the time there is a mistake it would actually hurt me if I always assumed that cb was making a mistake when my answer wasnt present so the answers 12pi</p>

13

<p>Ohh, ok thank you very much ssimone</p>