10-7 Areas of Circles and Sectors Objective To find the areas of circles, sectors, and segments of circles.

10-7 Areas of Circles and Sectors

ObjectiveTo find the areas of circles,

sectors, and segments of circles

What is…

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a) d b) r c) 2r d) r2

Theorem 10-11 Area of a Circle

• The area of a circle is the product of π and the square of the radius.

What is the area of a circle with 15 cm radius?

Ex. 1 How much more pizza is in a 12 in. than a 10 in pizza

• Find the areas of each and subtract

Sector of a circle

The region bounded by 2 radii and their intercepted arc

Ex would be a slice of pizza Sectors are named by using one

endpoint of the arc, the center, and the other endpoint

Theorem 10-12 Area of a sector of a circle

The area of a sector of a circle is the product of the ratio (measure of arc/360) and the area of the circle.

𝑨𝒓𝒆𝒂=𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒐𝒇 𝒂𝒓𝒄

𝟑𝟔𝟎∙𝝅 𝒓𝟐

Ex. 2Z

O

M

72°

r = 5 in

Ex. 3

Circle has a d = 20 cm. What is the area of a sector bounded by 208° arc? Round to the nearest tenth.

Segment of a circle

• Part of a circle bounded by an arc and the segment connecting its endpoints

To find the area of a segment

• 1st draw in the radii to form a sector.• 2nd find the area of the sector• 3rd find the area of the triangle• 4th subtract (sector-triangle)

Ex. 4A

OB

10 in

Ex. 5 radius is 12cm and 60° arc.

Find the area of the segment

60°

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CLASSWORK

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