In a circle with a radius of 6 m, an arc is intercepted by a central angle of 7π/4 radians.
What is the arc length?
Use 3.14 for π .
To find the arc length, we can use the formula:
Arc length = (angle / 2π) * circumference
Given:
Radius (r) = 6 m
Central angle (θ) = 7π/4 radians
π ≈ 3.14
We need to find the circumference first:
Circumference = 2πr
Substituting the given value of r:
Circumference = 2 * 3.14 * 6
Circumference = 37.68 m
Now, we can calculate the arc length:
Arc length = (θ / 2π) * circumference
Arc length = (7π/4 / 2π) * 37.68
Arc length = (7/4) * 37.68
Arc length = 65.73 m (rounded to two decimal places)
Therefore, the arc length is approximately 65.73 m.
To find the arc length, we can use the formula:
Arc Length = Radius × Central Angle
Given that the radius of the circle is 6 m and the central angle is 7π/4 radians, we can substitute these values into the formula:
Arc Length = 6 m × (7π/4)
Next, we can simplify the expression by multiplying the numbers:
Arc Length = 42π/4
Since we need to use the value of π as 3.14, we can substitute it:
Arc Length ≈ 42 × 3.14 / 4
Now, we can calculate the approximate value of the arc length:
Arc Length ≈ 32.94 m
So, the arc length is approximately 32.94 m.
arc length = π r Ø
where r is the radius, and Ø is the central angle measured in radians
You have all the data.
actually, arc length = rØ
the whole circle has circumference 2πr.