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# 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

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

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

### 1 Answer

- 1 decade agoFavorite Answer
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)