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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

8. Geometric Probability

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Exercise 52 Page 674

A sector of a circle is the region bounded by an arc of the circle and the two radii to the arc's endpoints. The area of a sector of a circle is the product of the area of the circle and the measure of the arc divided by 360.

12πcm^2

Practice makes perfect

A sector of a circle is the region bounded by an arc of the circle and the two radii to the arc's endpoints.

The area of a sector of a circle is the product of the area of the circle and the measure of the arc divided by 360.

Area of sectorAOB: m AB/360* π r^2

Recall that the measure of a minor arc is equal to the measure of its corresponding central angle. We are told that the central angle measures 30^(∘). Therefore, the measure of its corresponding arc is also 30^(∘).

We want to find the area of sector AOB in ⊙ O. We are given that the radius of the circle is 12 centimeters and we know that the measure of its corresponding arc is 30^(∘). Therefore, we have all the information we need to use the formula to find the area of sector AOB.

A= mAB/360* π r^2

mAB= 30, r= 12

A=30/360* π ( 12^2)

▼

Evaluate right-hand side

Calculate power

A=30/360* π (144)

CommutativePropMult

Commutative Property of Multiplication

A=30/360* 144π

MoveRightFacToNum

a/c* b = a* b/c

A=4320/360π

Calculate quotient

A=12π

We found that the area of the sector is 12π square centimeters.

Subchapter links

Lesson Check p.671

Practice and Problem-Solving Exercises p.671-673

Standardized Test Prep p.674

Mixed Review p.674