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How to Solve the Value of Radius given the Angle and Arc length?

TopAnswer to question how to solve the value of radius given the angle and arc length, is shown below with help of steps:
Step 1: First, we calculate center angle of given Geometry, which is generally given in question like we have a Circle geometry, whose center angle is 60 degree.
Step 2: After center angle of given geometry, we calculate arc length of given geometry, which is also given in question like Arc Length of Circle geometry is 7.33 inch.
Step 3: After first two steps, we use following formula for evaluation of Radius of Circle.
Arc length of geometry (s) = radius of geometry (r) * center angle of geometry (θ).
= > radius of geometry (r) = Arc length of geometry (s) / center angle of geometry (θ).
We take an example, which define whole process for calculation of radius of given geometry –
Example: An arc length of circle is 8.33 inch and center angle of circle is 120 degree, then find the radius of given circle?
Solution: we use following steps for evaluating the radius of given circle–
Step 1: Firstly, we calculate center angle of given geometry, here center angle of circle is 120 degree. So, center angle of circle (θ) = 120 degree = (2 * Π) / 3 = 2.09 radian.
Step 2: After center angle of given geometry, now we calculate arc length of given geometry, here arc length of circle geometry is 8.33 inch.
Step 3: After first two steps, we use following formula for evaluation of radius of circle –
Arc length of circle (s) = radius of circle (r) * center angle of circle (θ),
=> Radius of circle (r) = Arc length of circle (s) / center angle of circle (θ),
=> Radius of circle (r) = 8.33 / 2.09,
=> r = 3.98 inch,
So, radius of circle is 3.98 inch.