## Circle E has a radius of 40 inches with = 324°. Find the exact length of

Question

Circle E has a radius of 40 inches with = 324°. Find the exact length of

0

72 π inches

Step-by-step explanation:

1) Set up a ratio: 324/360. Simplify it: 9/10.

2) Then do: 9/10 x 2 π r  –>  9/10 x 2 π 40. You should get: 72 π.

3) So, the exact length of arc ABC = 72 π inches.

(The reason you are supposed to leave it 72 π inches is because only if the question asks you to find the approximate length of the arc, then you can use 3.14 instead of π. But if the question asks you to find the exact length of the arc, you have to leave it as said above because you would still have to round the answer (if you multiply 72 by pi), which makes it an approximate answer, not an exact answer.)

pi (π) = 3.14159265359………………….

Pi is an endless number.

Hope this helps!   🙂

2. Let the arc is ABC with angle 324 degree, to find the length of that arc follow the steps;
The circumference of the circle E is :C = 2 r π
C = 2 * 40 π = 80 π cm.
Also 324° / 360° = 0.9m Arc (ABC ) = 0.9 * 80 π = 72 π cm
There is also formula for calculating the measure of an arc:
m Arc = r π α / 180°
m Arc = 40 π * 324 / 180
= 40π * 1.8 = 72 π
Now we have to find the exact length ( π ≈ 3.14 )
m Arc ( ABC ) = 72 * 3.14 = 226.08 cm