Question

What is the exact length of arc AB?

π m
4π m
8π m
2π m

Answer 1

Find the circumference of the entire circle.
Then use the fraction of the circle that corresponds to that arc.
A full circle corresponds to a central angle of 360 degrees.
You only want 45 degrees of that arc.

Answer 2

@mathstudent55 would it be 4?

Answer 3

FORMAL FORMULA:

θ/360 × 2 × π × r
45/360*2*pi*r
0.125*2*r*pi
0.125*2*4*pi
1pi
πm

Answer 4

am i right @mathstudent55

Answer 5

I believe your answer is correct @dannyrod2000 . Not sure if mathstudent55 is gonna reply lol

Answer 6

The circumference of the circle is

\(2 \pi r = 2 \pi \times 4 ~m = 8 \pi ~m\)

The fraction of the circumference is:

\(\dfrac{45^\circ}{360^\circ} = \dfrac{1}{8}\)

Now you multiply the fraction by the entire circumference:

\(\dfrac{1}{8} \times 8 \pi~m = \pi ~m\)

You are correct. The answer is \(\pi ~m\).