11.3 Area of Circles and Sectors

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Presentation transcript:

11.3 Area of Circles and Sectors

Section 11.3 ~ Areas of Circles and Sectors Objectives: Be able to find the area of circles and sectors!! Quick Review: Z L M N O Name the following from circle Z. Minor arc: Major arc: Semicircle: Radius: Diameter: ON, NM, ML, OM, NL OLM, OLN, MNL, MOL, NOL, NOM, NLM OL OZ, NZ, MZ, LZ OL

Theorem The equation for the Area of a Circle Area equals radius squared times pi.

Theorem The equation for the Area of a Circle Area equals pi times radius squared.

Area of a Circle! More Vocab: Find the area of each circle. Leave answers in terms of π. 14 in. 10 in. 12 in. More Vocab: Sector of a circle: A O B sector AOB region bounded by an arc and the two radii touching its endpoints

Definition of a Circle Sector A circle sector is a fraction of the circle enclosed by two radii and an arc.

The Equation for the Area of a Sector

The Equation for the Area of a Sector

Sector CZD Sector BZC Sector BZA A Z B 18° D C 72° Find the area of each sector. Leave answers in terms of π. Sector CZD Sector BZC Sector BZA Z A D C B 72° 20 cm 18°

Find the Radius The Sector Area is 𝟏𝟓𝝅 𝑪𝒆𝒏𝒕𝒓𝒂𝒍 𝑨𝒏𝒈𝒍𝒆 𝒊𝒔 𝟏𝟓𝟎° 𝑆𝑒𝑐𝑡𝑜𝑟= 𝜃 360 ( 𝑟 2 𝜋) 𝑟 2 =15( 12 5 )→36 15𝜋= 150 360 ( 𝑟 2 )𝜋 𝑟 2 =36→ 𝑟 2 =± 36 15= 5 12 𝑟 2 𝑟=6

Challenge Problems! Find the area of each shaded region. Leave answers in terms of π. 15 cm 10 in.

Do you know your formulas? Circumference: Arclength: Area: Area of sector: