Question

Find the length of the arc shown in brown. Leave your answer in terms of pi.

Answer 1

Answer:1. a central angle

2. c 270

3.d. Two times r equals the diameter of the circle. Pi equals the circumference divided by the diameter. When you multiply, the diameter is in both the numerator and the denominator, which cancels out, leaving the circumference.

4. c 155

5. c 70

6.b 55

7. c 19 in

8. a 183.3 ft

9. b 8 pi ft

10. b 33 pi in

Explanation:

Answer 2

The central angle that captures the brown arc is 120°. To find out what fraction of the total circumference the brown arc is, we can find the ratio of this 120° angle to the total central angle of a circle, which is 360°. So we have:


`(120)/(360) = (1)/(3)`

Now we know the brown arc is
`(1)/(3)` of the total circumference. The circumference is π*diameter, so in this case it’s 24π.

Finally, we do:


`(1)/(3)*24 \pi =8 \pi \text{ feet}`