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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 39 Page 796

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.

175.8in.^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 We want to find the area of sector WXY in ⊙ X. We know that the radius of the circle is 9.4in. and that the measure of its corresponding arc is 228^(∘).

We have all the information we need to use the formula to find the area of sector WXY.

A=228/360* π ( 9.4^2)

▼

Evaluate right-hand side

Calculate power

A=228/360* π (88.36)

CommutativePropMult

Commutative Property of Multiplication

A=228/360* 88.36π

MoveRightFacToNum

a/c* b = a* b/c

A=20146.08π/360

Use a calculator

A=175.8077137 ...

Round to 1 decimal place(s)

A=175.8

Therefore, the area of the sector measures 175.8 in.^2

Subchapter links

1 Circles and Circumference p.792

2 Measuring Angles and Arcs p.792

3 Arcs and Chords p.793

4 Inscribed Angles p.793

5 Tangents p.794

6 Secants, Tangents, and Angle Measures p.794

7 Special Segments in a Circle p.795

8 Equations of Circles p.795

9 Areas of Circles and Sectors p.796