The Student Room Group

Radian measure+sectors, secments...C2. Pls help me!!!

Please can someone help me with these Qs:

10) A chord AB subtends an angle of (theta) radians at the centre O of a circle of radius 6.5cm. Find the area of the segment enclosed by the chord AB and the minor arc AB, when:
a) theta=0.8
b) theta=2/3 Pi
c) theta= 4/3 Pi

11) An arc AB subtends an angle of 0.25 radians at the circumference of a circle, centre O and radius 6 cm. Calculate the area of the minor sector OAB.

13) A sector of circle of radius 28 cm has perimeter P cm and area A cm^2. Given that A=4P, find the value of P.
Reply 1
10) can be worked out by using area of segment=1/2 r^2 theta minus the area of the triangle (1/2 acSinB)

i.e. if theta=0.8 and radius=6.5cm, area of segment is:
(0.5x6.5^2x0.8)-(0.5x6.5x6.5xSin0.8)=16.9-15.15=1.75(3sf)

The rest can be worked out in this fashion

11) Area of sector=0.5xr^2xtheta=0.5x36x0.25=4.5

13) Area=1/2r^2theta=392theta

Perimeter=length of arc+(2xradius)=rtheta+56=28theta+56

P=28theta+56
A=392theta
A=4P

392theta=4(28theta+56)
392theta=112theta+224
280theta=224
theta=0.8

P=28theta+56=22.4+56=78.4cm

I might have made some mistakes because its be that kind of week, but thats the method anyhow.
Reply 2
please???
Reply 3
ooo thanks!