Question

The formula for the circumference of a circle is
C
=
where
C
= circumference and
= diameter. Itcan also be defined as
C
= 2
where
=radius. If 360 degrees = 2
radians, and the proportionalrelationship
=
, is given and
= arc length, then determine the length created by a 60 degree centralangle in a circle with a 10 inch diameter and explain how you found it. Leave your answer in terms ofpi. You may type out your work or upload it.
Which of the following would be the best way to answer this question for full credit?
(1 point)
πd d
πr r π
θ s
r
s
The answer is
because we plugged in the known angle of 60 degrees in terms of radians by taking
or simplified to
of 2
to get
as the central angle in terms of radians. Next, we use the knownproportional relationship replacing the angle and radius of 5 as it is half of the diameter given to get
. By multiplying both sides by 5 we solve for our arc length and get
5
π
3
60
360
1
6
π
π
3
=
π
3
s
5
=
s
5
π
3
The answer is 5.24
I don't know
I'd leave this question blank even though it is worth 3 points and will hurt my overall grade by a lot for notattempting it.

Answer 1

Choose the method that uses s = r·θ.

Work:
- Diameter = 10, so radius r = 5.
- Convert 60° to radians: 60° = (60/180)π = π/3.
- Arc length s = r·θ = 5·(π/3) = 5π/3 inches.

So the best answer is the one that uses s = rθ and gives s = 5π/3.