## anonymous one year ago 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.

1. phi

when you say "own AB" do you mean "arc AB" ?

2. anonymous

I believe so

3. phi

there is an expression $r \theta = s$ which means radius times the angle (in radians) = the length of the arc

4. 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 $\theta = \frac{arc\ AB}{r} = \frac{\pi}{10}$

5. anonymous

I'm following

6. phi

I think you want the ratio of theta (the angle of the sector) divided by 2pi (the angle of the whole circle)

7. phi

or instead of dividing theta by 2pi, multiply by 1/(2pi)

8. phi

the idea is the angle of sector / 2pi is the fraction of the whole circle we want to know $\frac{\pi}{10} \cdot \frac{1}{2 \pi}$

9. anonymous

So I would solve that?

10. 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)

11. anonymous

So replace both pi with 1 (I'm trying to fully understand ^^;)

12. 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 $\frac{3\cdot 2}{3} = \frac{3}{3} \cdot 2 = 1 \cdot 2 = 2$

13. phi

think of the pi as the "3" in that example $\frac{\pi}{10} \cdot \frac{1}{2 \pi} = \frac{\pi}{\pi} \cdot \frac{1}{10 \cdot 2}$

14. phi

2pi means 2 * pi so the top is 1*pi the bottom is 2*10*pi and the pi's cancel

15. 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)

16. phi

the top simplifies to 1 the bottom to 2*10 which (I assume) you know is 20

17. anonymous

Thank you so much

18. phi

yw