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Find the radian measure of the central angle of the circle of radius 6 cm that intercepts an arc of length 32 cm.

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Answer:

formula to use: s=rx, s=arc, r=radius, x=central angle in radians

32=6x

x=32/6=16/3 radians

Step-by-step explanation:

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The radian measure of the central angle of the circle is 5.33 rads

A circle is the locus of a point such that its distance from a fixed point is constant.

The arc length is given by:

Arc length = θ * r

Where r is the radius and θ is the central angle in radians.

Given an arc length of 32 cm and radius of 6 cm, hence:

Arc length = θ * r

32 = θ * 6

θ = 5.33 rads

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