Question

help!!

Find the arc length intercepted by a central angle of 3x/4 radians in a circle whose radius is 18.4 inches.


13.8π
15.2π
24.5π

Answer 1

Do you mean 3pi/4 instead of 3x/4???

Answer 2

@Mertsj yes! omg im sorry ):

Answer 3

What part of the circle is an angle of 3 pi/4

Answer 4

yeah the thing is that im not sure what part of a circle is "arc length intercepted by a central angle"

Answer 5

\[\frac{\frac{3\pi}{4}}{2\pi}\]

Answer 6

If you simplify that complex fraction you find that the angle we are talking about is 3/8 of the entire circle.

Answer 7

So our job is to find the length of the arc intercepted by that angle.
To do so you need to find the length of the entire circle (which is called circumference) and multiply it by 3/8.

Answer 8

so it would be 2pi multiply by 3/8 maybe...?

Answer 9

Did you notice that I said to find the circumference of the circle?

Answer 10

c=pi*d right??

Answer 11

yes

Answer 12

then would i plug in 3/8 in d?

Answer 13

The diameter is twice the radius which is given

Answer 14

\[\theta =\frac{ l }{ r },l=r \theta=\frac{ 3\pi }{4 }*18.4=13.8\pi \]