in a circle of radius 26, find the length of the arc spanned by a central angle of pi/4 radians. round your answer to 2 decimal places. use 3.1416 as an approx for pi.
Recall that C = rθ
Remember that for a whole circle, θ=2π, so C = 2πr
Here, we have r = 26, θ=π/4
c = 26 * π/4 = 13/2 * π = 20.42
To find the length of the arc spanned by a central angle of π/4 radians, we can use the formula:
Arc Length = Radius × Central Angle
Given that the radius of the circle is 26, and the central angle is π/4 radians, we can substitute these values into the formula:
Arc Length = 26 × π/4
Now, let's calculate the value:
Arc Length = 26 × 3.1416/4
Arc Length ≈ 20.42
Rounding the answer to 2 decimal places gives us the length of the arc as approximately 20.42 units.
To find the length of the arc spanned by a central angle in a circle, you can use the formula:
Arc Length = (Central Angle / 2π) * (2πr)
Where:
- Central Angle is the measure of the angle in radians
- r is the radius of the circle
Given:
- Radius of the circle, r = 26
- Central Angle, θ = π/4 radians
Using the formula, you can substitute the values and calculate the length of the arc:
Arc Length = (π/4 / 2π) * (2π * 26)
= (1/4) * (2 * 3.1416 * 26)
= (1/4) * (160.9344)
= 40.2336
Rounding the answer to 2 decimal places, the length of the arc spanned by a central angle of π/4 radians in a circle of radius 26 is approximately 40.23 units.