The radius of the circle is 36 centimeters when the arc length is 32 centimeters and the corresponding central angle is (8/9)π radians.
What is an arc of the circle?
A circle's arc is defined as a portion or segment of its circumference.
How is the length of an arc calculated?
The length of an arc, s. of a circle having a radius r, with the central angle θ, is given as s = rθ.
How to solve the question?
In the question, we are given an arc of a circle having a length (s) = 32π centimeters, and the corresponding central angle (θ) = (8/9)π radians.
We are asked to find the radius (r) of the circle.
We know that the arc length is the product of the radius and the central angle, that is, s = rθ.
Following this, we can write:
32π = r(8/9)π,
or, r = (32π*9)/(8π) = 36.
Therefore, the radius of the circle is 36 centimeters.
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