Question

it looks long but im just explaining what i did and can someone please tell me where i went wrong???
PLEASE?

ok, a sector of a circle of radius 6 cm has an angle of 1.6 radians
find the area for the sector hence find the area of the segment

The problem is that i worked out the area which is 28.8 of the sector

i worked out the triangle and took it away from the area of the sector and ended up with 10.8 which is right but then here's the problem how do you use the formula of the area of the sector?
it 1/2x6^2xsin(1.6)=0.50258...
but that not what i got above i got 10.8 above :S

Answer 1

the area of a sector is the same as that of a circle; you just replace the angle measurement...

2pi r^2
------- = area circle
2

angle r^2
-------- = area any part of a circle
2

Answer 2

1.8pi 6^2
------- = .9pi(36) = 32.4 pi
2

Answer 3

ack!!...forget the pi part lol

Answer 4

32.4

Answer 5

so is the formula wrong then?

Answer 6

dunno; but my inputs are dyslexic...

1.6 (36)
------- = area of sector
2

Answer 7

.8(36) = 28.8

Answer 8

but thats a different answer :(
so is 10.8 wrong then??

Answer 9

why are you removing the area of the triangle?

Answer 10

to get the segment area
and i looked at the mark scheme and 10.8 is right but theres a segemnt area formula and that doesnt work :(

Answer 11

so teh segment will be the arch looking section of the piece of pie right?

Answer 12

the area of a trianlge is:

r^2 sin(angle)
------------
2

Answer 13

make sure you have your calculator set to radians tho

Answer 14

sin??
isnt area of a traingle BxH/2???

Answer 15

it is; but this isnt the area of a right triangle

Answer 16

oh :o

Answer 17

the area of any triangle is:

base = radial arm = 6

height = radial arm *sin(a) = 6 sin(1.6)

and /2

sooo...

36 sin(1.6)
--------- = 18 sin(1.6)
2

Answer 18

the area of the tri is abt: 17.99

Answer 19

here is the diagram, if u need it

Answer 20

28.8
-17.99
-------
10.81

Answer 21

or maybe not..... is 1.2 larger than 90?

Answer 22

1.2 lager than 90???
is this a trick qs?

Answer 23

1.2 * 180
-------- = 68.75 degrees right?
pi

Answer 24

yes, but now im lost where did you get these number fomr?

Answer 25

trying to convert radians to degrees;

radians normally have a pi in them so you multiply by 180/pi to get the angle..

pi 180
-- * ----- = 90 degrees
2 pi

Answer 26

12 180
--- * ---- = 216/pi = 68.75
10 pi

Answer 27

oh :o

Answer 28

since the angle is acute; we can assume that our method was correct;

Answer 29

so I get 10.81

whats the answer you get?

Answer 30

10.8 :)

Answer 31

then the area of the segment should be 10.8 :)

Answer 32

thank you soo much for explaining this :)

if i could i would have wanted to give you some more medals but i can only give you one :S

Answer 33

'sok; you enjoy yourself now :) i got class starting soon

Answer 34

bye bye :)