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An arc of circle M has a length of 32π centimeters and the corresponding central angle has a radian measure of 8/9π. What is the radius of the circle?

Sagot :

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Answer:

36 cm

Step-by-step explanation:

arc length = r × θ


32π = r × 8/9π

r = 36

anuksha0456

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.

Learn more about arc length at

https://brainly.com/question/2005046

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