anonymous
  • anonymous
I'm not fully understanding this and need help. Points A and B lie on a circle centered at point O. If length of own AB/radius=π/10, what is the ratio of the area of sector AOB to the area of the circle? A.) 1/10 B.) π/10 C.) 1/20 D.) π/20 I already know B isn't the answer. I'm thinking A is.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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phi
  • phi
when you say "own AB" do you mean "arc AB" ?
anonymous
  • anonymous
I believe so
phi
  • phi
there is an expression \[ r \theta = s\] which means radius times the angle (in radians) = the length of the arc

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phi
  • phi
for your problem, where we use arc AB instead of "s" \[ r \theta = arc AB \] if we divide both sides by r we get \[ \theta = \frac{arc\ AB}{r} \] the question says that is pi/10 \[ \theta = \frac{arc\ AB}{r} = \frac{\pi}{10}\]
anonymous
  • anonymous
I'm following
phi
  • phi
I think you want the ratio of theta (the angle of the sector) divided by 2pi (the angle of the whole circle)
phi
  • phi
or instead of dividing theta by 2pi, multiply by 1/(2pi)
phi
  • phi
the idea is the angle of sector / 2pi is the fraction of the whole circle we want to know \[ \frac{\pi}{10} \cdot \frac{1}{2 \pi} \]
anonymous
  • anonymous
So I would solve that?
phi
  • phi
strictly speaking you only solve equations (which have = signs) in this case, you simplify. notice you have a pi "up top" and "down below" which means pi/pi = 1 (i.e. it cancels) to multiply the fraction, you multiply top time top and bottom times bottom (and of course simplify pi/pi to 1)
anonymous
  • anonymous
So replace both pi with 1 (I'm trying to fully understand ^^;)
phi
  • phi
it works the same way as with numbers. for example if you had 6/3 (which we know is 2) but we write it as \[ \frac{3\cdot 2}{3} = \frac{3}{3} \cdot 2 = 1 \cdot 2 = 2\]
phi
  • phi
think of the pi as the "3" in that example \[ \frac{\pi}{10} \cdot \frac{1}{2 \pi} = \frac{\pi}{\pi} \cdot \frac{1}{10 \cdot 2} \]
phi
  • phi
2pi means 2 * pi so the top is 1*pi the bottom is 2*10*pi and the pi's cancel
anonymous
  • anonymous
Oh I understand it now. The pi would cancel out and then the answer would pretty much be right in front of you. (As you just said)
phi
  • phi
the top simplifies to 1 the bottom to 2*10 which (I assume) you know is 20
anonymous
  • anonymous
Thank you so much
phi
  • phi
yw

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