The formula for circumference of a circle is C equals pi D where C equals circumference and D equals diameter it can also be defined as C equals two pi R where are equals radius if 360° equals two pi radians and the formula for length is zero equals SR then determine the length created by a 60° central angle in a circle with a 2 inch diameter and explain how you found it answer
To find the length created by a 60° central angle in a circle with a 2 inch diameter, we first need to find the circumference of the circle.
Given that the diameter is 2 inches, the radius (R) is half of the diameter, so R = 1 inch.
Using the formula C = 2πR, plug in the radius:
C = 2π(1)
C = 2π inches
Now, since 360° equals 2π radians, we can convert the central angle of 60° into radians:
60° * (2π/360°) = π/3 radians
Next, we need to find the arc length created by a central angle of π/3 radians. The formula for arc length (l) is l = rθ, where r is the radius and θ is the central angle in radians.
Plug in the values:
l = 1 * (π/3)
l = π/3 inches
Therefore, the length created by a 60° central angle in a circle with a 2 inch diameter is π/3 inches or approximately 1.047 inches.