The formula for circumference of a circle is C equals PD where C equals circumference and D equals diameter it can also be defined as C equals two pi R where radius equals R equals radius 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
To determine the length created by a 60° central angle in a circle with a 2-inch diameter, we first need to calculate the circumference of the circle using C = πd, where d is the diameter.
Given that the diameter is 2 inches, we can find the radius by dividing the diameter by 2:
Radius (R) = 2 inches / 2 = 1 inch
Now, we can calculate the circumference of the circle using C = 2πR:
C = 2π(1) = 2π inches
Next, we need to find the length created by a 60° central angle. To do this, we will first calculate what fraction of the circle the 60° angle represents:
Fraction of the circle = 60° / 360° = 1/6
Now, we can find the length created by the 60° central angle by multiplying the fraction of the circle by the circumference:
Length = (1/6) * 2π inches = π/3 inches
Therefore, the length created by a 60° central angle in a circle with a 2-inch diameter is approximately π/3 inches.