What is the length of the circular arc intercepted by a central angle of 20degrees in a circle with a radius of 5cm?
your arc length is 20/360 or 1/18 of the circumference.
The circmf = 2π(5) = 10π
so the arc length = (1/18)(10π) = 5π/9 cm
To find the length of the circular arc intercepted by a central angle, we can use the formula:
Length = (Central angle ÷ 360) × (2π × Radius)
In this case, the central angle is 20 degrees and the radius is 5 cm. Substituting these values into the formula, we get:
Length = (20 ÷ 360) × (2π × 5)
To simplify the calculation, we can convert 20 degrees to radians by using the formula:
Radian = (Degree × π) ÷ 180
Radian = (20 × π) ÷ 180
Radian ≈ 0.3491
Now we can substitute the radian value into the formula:
Length = (0.3491 ÷ 360) × (2π × 5)
Length ≈ 0.0873 × 31.4159
Length ≈ 2.7481 cm
Therefore, the length of the circular arc intercepted by a central angle of 20 degrees in a circle with a radius of 5 cm is approximately 2.7481 cm.