## anonymous one year ago Find the area of the sector shown

1. anonymous

|dw:1436238473382:dw|

2. Vocaloid

well, we know that an entire circle is 360 degrees, and the sector we have is 80 degrees therefore, the area of the sector is (80/360) of the entire circle we multiply (80/360) times the area of the circle, where area = pi*r^2 putting it all together: area of sector = (80/360)*(pi)(r^2)

3. anonymous

i put the formula as (1/2) (8^2) (80) (pi/180)

4. Vocaloid

yeah, that works too. it should give you the same result in the end

5. anonymous

well i got 44.68 is that correct

6. Vocaloid

yeah that's right, good job

7. anonymous

are you sure that's correct because i checked the answer and it's supposed to be 35.45

8. anonymous

so i was confused

9. anonymous

@jdbruso

10. Vocaloid

@UsukiDoll I'm pretty sure I'm right, please check my work?

11. anonymous

i think so too but idk why it has a different answer

12. UsukiDoll

are we finding a semi-circle, quarter circle, or any sector (which is a fractional part of the area)?

13. anonymous

any sector

14. UsukiDoll

alright so the formula for the area for circle is $A= \pi r^2$ But for any sector we either use the formula $A= \frac{n}{360} \pi r^2$ which is n is the number of degrees in the central angle of the sector or $A= \frac{C_s}{2 \pi r} \pi r^2$ where C_s is the length of the sector

15. UsukiDoll

|dw:1436239304856:dw| so you're given 80 degrees.. that's your n and you have a radius of 8

16. anonymous

i got the same answer with both those formulas

17. anonymous

im guessing that the book just has it wrong then

18. UsukiDoll

$A= \frac{80}{360} \pi (8)^2$ $A= \frac{2}{9} \pi( 64)$

19. UsukiDoll

20. UsukiDoll

I also have the same answer as @Vocaloid

21. anonymous

yeah same here

22. anonymous

thank you!

23. UsukiDoll

$A= \frac{2}{9} \pi( 64)$ $A= \frac{128}{9} \pi$ $A= 14.222222222222222\pi$ $A=44.68$

24. anonymous

yeah you're right we all go the same answer