11.5 Areas of Circles &amp; Sectors

# 11.5 Areas of Circles &amp; Sectors - 11.5 Areas of...

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Unformatted text preview: 11.5 Areas of Circles & Sectors Sectors p. 691 Thm 11.7 – Area of a Circle – Thm Area A = π r2 * Remember to square the radius 1st, then multiply by π ! Ex: Find the area of circle C. Ex A = π r2 A = π (3)2 A = 9π cm2 OR 28.27 cm2 cm 3 C Ex: Find the diameter of circle C Ex Find 2 if the area is 16π ft . if A = π r2 16π = π r2 16 = r2 ð 16 = r 4 ft = r So, d = 8 ft. Sector of a Circle Sector • The region bounded by 2 radii & their The intercepted arc. intercepted Sector Also a sector • Visually, it might remind you of a slice Visually, of pizza or a piece of pie. of Thm 11.8 – Area of a Sector – Thm Area arc measure 2 A= ∗ πr o 360 Ex: Find the area of the small sector Ex Find shown. shown. arc measure 2 A= ∗ πr o 360 11 m 135 2 A= ∗π (11) o 360 135 A= ∗121π 360 o 135o A = 142.55 m 2 Ex: L & M are 2 pts. on a circle R with Ex are r=50 cm & m∠ LRM=150o. Find the areas r=50 Find of the sectors formed by ∠ LRM. arc measure AI = ∗ πr 2 360 o 150 2 AI = ∗ π ( 50 ) 360 II R L arc measure AII = ∗ πr 2 360o 50 cm o 150 210 2 AII = ∗ π ( 50) 360 M AI = 3272.49 cm 2 I AII = 4581.49 cm 2 Ex: Find the area of the shaded region. Ex Ao − A∆ = Ashaded region 4c m π r2 π (4)2 16π (4 3 ) 4 s2 3 4 2 3 = 16 ∗ 3 ∗ 3 4 = 48 3 4 = 12 3 2 4c m 16π - 12ð 3 = 29.5 cm2 29.5 30o 2ð 3 4ð 3 Assignment Assignment ...
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