How do i do the question in the image below? p37

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Answer 1 · 2018-02-09T04:21:32

Area of the minor segment cut off by the chord AB (shaded por enter image source here tion in the figure) is #color(green)(292.705#

Given : #OA = OB = r = 18 cm, OhatAB = 20^0#

To find the area of the shaded portion.

#OhatAB = OhatBA = 20^0 as OB = OA = r#

#AhatOB = theta = 180 - 20 - 20 = 140^0#

#vec(AB) /2 = r sin( theta/2) = 18 * sin 70 ~~ 16.91#

#vec(AB) = 2 * 16.915 = 33.83#

Area of sector OAB #= (theta/360) * pi r^2 = (140/360) pi 18^2 = 395.84 cm^2#

Area of triangle OAB #= (1/2) (AB) * (OA) cos (theta/2) = (1/2) 33.83 * 18 cos (70) = 104.135 cm^2#

Area of the shaded portion #= 396.84 - 104.135 = color(green)(292.705#