Calculate the area of the dark part of

Calculate the area of the dark part of his circle. The radius is 12. 5 m long. 368. 16 m 2 (1 dp)

1 radian = the angle formed in a sector with the arc length the same as the radius 1 radian The length of an arc is proportional to both: • The angle at the centre of the arc • The radius of the arc Θ s 2θ 2 s Θ s θ 3 s r 3 r Two sectors have the same radius Two sectors have the same centre angle

Arc Length Formula s = rθ s s = arc length r = length of radius Θ = angle at centre of sector, r θ measured in radians r Rearranging the arc length formula, we have: angle = arc length or θ = s radius r

Conversion of degrees/radians 1800 00 0 π 3600 = 2 π To convert degrees to radians, multiply by 2π so 1800 = π To convert radians to degrees, multiply by

Convert 450 to radians. Leave your answer in terms of π Answer 450 = 45 x = x π = Convert radians to degrees. Answer = 2 x 180 = 360 = 1200 3 Using the arc length formula calculate the length of the arc ABC s = rθ so ABC = rθ = 8 x = cm or in decimal form 20. 1 cm (1 dp) B A 8 cm C

Calculate the size of the angle labelled θ in degrees. 6 5 θ 5

Sector area formula Area A = ½ r 2 θ (note θ is in radians) Π 2 cm 3 Answer The angle at the centre of the shaded sector is 2 cm 2π - = Area of sector = ½ x 22 x = cm 2 or 10. 47 cm 2 (4 sf) The sector area formula can be rearranged to make either θ or r the subject 2 A = r 2θ Θ = r =

Area of Segment The Area of a Segment is the area of a sector minus the triangular piece. Your calculator must be set in radians Area of Segment = ½ × (θ - sin θ) × r 2 = ½ × ( (θ × π/180) - sin θ) × r 2 (if θ is in degrees)