MATH SOLVE

4 months ago

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

Accepted Solution

A:

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:

[tex] \frac{120}{360} = \frac{1}{3} [/tex]

Now we know the brown arc is [tex] \frac{1}{3} [/tex] of the total circumference. The circumference is π*diameter, so in this case it’s 24π.

Finally, we do:

[tex]\frac{1}{3}*24 \pi =8 \pi \text{ feet}[/tex]

[tex] \frac{120}{360} = \frac{1}{3} [/tex]

Now we know the brown arc is [tex] \frac{1}{3} [/tex] of the total circumference. The circumference is π*diameter, so in this case it’s 24π.

Finally, we do:

[tex]\frac{1}{3}*24 \pi =8 \pi \text{ feet}[/tex]