anonymous
  • anonymous
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Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
@shamil98
anonymous
  • anonymous
A= big semicircle.. what's next?
anonymous
  • anonymous
50pi

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anonymous
  • anonymous
Just remove the semicircle on the left and place it in the gap on the right
anonymous
  • anonymous
this is SAT yes? I remember this one
anonymous
  • anonymous
\[a= \pi*r ^{2}\] \[a= ( \pi * 10^{2} ) /2 = 157.079\]
anonymous
  • anonymous
Isn't it right?
anonymous
  • anonymous
|dw:1389510061781:dw|
anonymous
  • anonymous
|dw:1389510085539:dw|
anonymous
  • anonymous
|dw:1389510103621:dw| so the area is equivalent to just the top semicircle... we merely moved the piece under the line to fill the hole to the right
anonymous
  • anonymous
the radius is very clearly \(r=10\) ergo the area is \(A=\pi r^2=\pi(10)^2=100\pi\)
anonymous
  • anonymous
|dw:1389510292746:dw|
anonymous
  • anonymous
It is a semicircle so you need to divide by 2. The answer is 50pi + 25pi over 2. \[\frac{ 75\pi }{ 2 }\] is the answer.
anonymous
  • anonymous
oops -- good catch. you do need to multiply by \(1/2\) to get just the top:$$\frac12\cdot100\pi=50\pi$$that being said, it is NOT \(\frac12(50\pi+25\pi)\)
anonymous
  • anonymous
|dw:1389510798177:dw|
anonymous
  • anonymous
so.. also find that part and add it?
anonymous
  • anonymous
You need to add that because it is also shaded. The area of that part is 25pi over two.
anonymous
  • anonymous
@liliegirl that part is precisely the part we moved to fill in the top semicircle. it is now accounted for...
anonymous
  • anonymous
oh. right
anonymous
  • anonymous
so.. the answer is.. 314.16 right? thanks guys
anonymous
  • anonymous
@oldrin.bataku Ahhh, Sorry, I didn't notice.... :)))
anonymous
  • anonymous
@stupidinmath no it's half of that, i.e. \(50\pi\)
anonymous
  • anonymous
oh.. since its a semi circle.. k thanks :)

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