Exercise 21 Page 758

The length of an arc of a circle is the product of the measure of the arc divided by 360 and the circumference of the circle. length of AB=mAB/360 * π d

Let's consider the given circle.

We can see that the diameter of the circle is 12 and mAB=90^(∘). If we let A and B be the endpoints of our arc, we can substitute mAB= 90 and d= 12 in the formula for arc length and simplify.

Length of AB=mAB/360 * π d

SubstituteII

mAB= 90, d= 12

Length of AB=90/360 * π 12

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Evaluate right-hand side

CommutativePropMult

Commutative Property of Multiplication

Length of AB=90/360 * 12π

MoveRightFacToNum

a/c* b = a* b/c

Length of AB=1080π/360

ReduceFrac

a/b=.a /360./.b /360.

Length of AB=3π

The length of the arc is 3π.