Consider circle o, in which arc xy measures 16π cm. the length of a radius of the circle is 32 cm.
what is the circumference of the circle?
π units
what is the ratio of the arc length to the circumference?

what is the measure of central angle xoy?

Circumference: 64π

Ratio:      1 : 4

Measure of ∠xoy:  π/2    

Step-by-step explanation:

We are given an arc length of 16π.  Since it's in terms of pi, we use the formula

S = rФ    where r is the radius, and Ф is the measure of the angle in radians (in terms of pi)

We are given S = 16π and r = 32, plug those in and find Ф

16π = 32Ф

  16π/32 = Ф

       π/2 = Ф

This is the measure of the central angle.  

The angle is π/2 radians.  There are 2π radians in the circumference, so the circumference is 4 times the arc length created by the central angle.  (There are 4 halves in 2)  so the ratio of the arc length tothe circumference is 1 : 4

The formula for circumference is C = 2πr, where r is the radius, so we hace

C = 2π(32) = 64π

42.4

step-by-step explanation:

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