Maths question about Circle Sectors? Please help!!?

Hi,

The question is:

O is at the centre of the circle. The radius is 4 cm. Angle AOB is 70 degrees.

Calculate

a) The perimeter of the minor segment AOB

b) The area of the major segment AOB

Please help

Thanks

Update:

the questions is about sectors but thank you very much for your detailed answer :) part b got the correct answer for me!

Update 2:

the questions is about sectors but thank you very much for your detailed answer :) part b got the correct answer for me!

1 Answer

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  • 1 decade ago
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    is it sectors or segment are you asking? Coz your detailed question is asking segments, then I will assume u ask about segments.

    (a)

    perimeter of a segment = arc length + chord length.

    Arc length can be found by the circumference x angle at centre / 360

    Chord length can be found by cosine rule.

    Angle at centre = 70 degrees.

    Arc length = 2π(4) (70/360) = 4.887 cm

    By Cosine rule,

    (Chord length AB)² = (4)² + (4)² - 2(4)(4) cos70º = 21.055

    Chord length AB = 4.589 cm

    Perimeter = 4.887 + 4.589 = 9.476 cm

    (if you want sector perimeter, replace the chord length by 2r)

    (b) Area of major segment is the sector area + triangle area.

    Sector area = circle area x angle at centre / 360

    triangle area = (1/2) (a) (b) sin C

    where a, b are length of two sides, and C is the angle between a and b.

    Sector area = π(4)² (360-70)/360 = 40.49

    Triangle area = (1/2)(4)(4) (sin 70) = 7.52

    total area = 48.01 cm²

    (if you are asking about sector, take away the triangular area)

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