Consider a circle with a radius of 10 centimeters.What is the length of the arc that measures 60° for the given circle?
To find the length of the arc that measures 60° for a circle with a radius of 10 centimeters, we can use the formula:
Arc Length = (θ/360) x 2πr
where θ is the central angle in degrees, r is the radius of the circle, and π is a constant approximately equal to 3.14159.
Plugging in the values:
θ = 60°
r = 10 cm
Arc Length = (60/360) x 2π x 10
Arc Length = (1/6) x 2π x 10
Arc Length = (1/6) x 20π
Arc Length = 20π/6
Arc Length = 10π/3
Arc Length ≈ 10 x 3.14159 / 3
Arc Length ≈ 10.472 centimeters
Therefore, the length of the arc that measures 60° for a circle with a radius of 10 centimeters is approximately 10.472 centimeters.