Find the length of arc XPY. Leave your answer in terms of π.

Question

1. 
   
2. A.
3. 2π m
4. 
   
5. B.
6. 12π m
7. 
   
8. C.
9. 6π m
10. 
    
11. D.
12. 360π m

I got C but, I'm not 100% sure

Answer 1

Good work ! Answer C is correct.

C=2*∏*r

C=2*∏*4

C=8∏

arc XPY is 270° because arc XY is 90°

you want 270/360 times the circumference

270/360=3/4

3/4 * 8∏=6∏ m for the length of arc XPY

Answer 2

You got it right. The length of the arc XPY is 3/4 of the length of the circle (this is because of the SIGN of a right angle). The length of the circle is 2 * pi * R (it is still good to know why) and your R is 4 m. Thus, The length of the arc XPY is

3/4 * ( 2 * pi * 4 m) = 6 * pi * m

Answer 3

Hello David,

First you will want to find the length of the entire circumference:

C = 2(3.14)r

r = 4

C = 2(3.14)4 = 8(pie)

Arc XPY is 3/4 of the entire circumference, so the Arc XPY would be 6pie...just like you got! : )