Maths question about Circle Sectors? Please help!!?

Question

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!

Answer 1

Favorite 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)