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C2 radians

Lunch_Box

def

(edited 10 years ago)

Reply 1

joostan

Original post by Lunch_Box

Figure 2 shows a circle of radius 12 cm which passes through the points P and Q.
The chord PQ subtends an angle of 120° at the centre of the circle.
(a) Find the exact length of the major arc PQ. (2)
(b) Show that the perimeter of the shaded minor segment is given by
k(2π + 3 3 ) cm, where k is an integer to be found. (4)
(c) Find, to 1 decimal place, the area of the shaded minor segment as a percentage
of the area of the circle.

for part c:

I am unsure why the answer has given the total area of the circle as pi*12^2 rather than 2pi*12^2?

Formula for area of circle = pi*r²

Reply 2

Lunch_Box

Original post by joostan

Formula for area of circle = pi*r²

Oh ffs i was thinking the forumla was theta*r^2

Reply 3

joostan

Original post by Lunch_Box

Oh ffs i was thinking the forumla was theta*r^2

lol dw everyone has their moments :tongue:

Reply 4

newyork newyork

can you please help me with part c.
The arc AB of a circle, centre O and radius r cm, is such that angle AOB = 0.5 radians.

Given that the perimeter of the minor sector of AOB = 30cm:
a) calculate the value of r- (the radius is 12)
b)show that the area of the minor sector AOB is 36cm^2
c) Calculate the area of the segment enclosed by the chord AB and the minor arc AB