The radius of a circle is 20. What is the length of an arc that subtends an angle of π/3 radians?
Give the exact answer in simplest form.
( π/3 / (2 π ) = 1/6 so 1/6 of the way around
so
(1/6) ( 2 π R) = (40/6) π = 20 π / 3
s = rθ = 10 * π/3 = 20π/3
To find the length of an arc in a circle, we can use the formula:
Arc Length = (θ/2π) * Circumference
Here, θ is the angle that the arc subtends at the center of the circle, and the circumference of the circle is given by 2πr, where r is the radius.
Given that the radius of the circle is 20, we can substitute the values into the formula:
Arc Length = (π/3/2π) * (2π * 20)
Simplifying, the π's cancel out:
Arc Length = (1/3) * (2 * 20)
Arc Length = (1/3) * 40
Arc Length = 40/3
So, the length of the arc that subtends an angle of π/3 radians is 40/3 units (in the same units as the radius).