Minor segment (1 Viewer)

[atakach99]

The length of an arc is 8.9 cm and the area of the sector is 24.3 cm squared when an angle of X is subtended at the centre of a cirlce. Find the area of the minor segment cut off by X, correct to 1 decimal place.

plz i need help solving this question
thnks

 

[tommykins]

A = [ r²(@-sin@) ]/2
L = r@

1. 8.9 = r@
24.3 = [ r²@ ] /2 -> 48.6 = r²@

Using the first equation, we try to find r.

@ = 8.9/r

r²(8.9/r) = 48.6

8.9r = 48.6

r = 48.6/8.9 = 5.46

Subbing this into the original 8.9 = r@

5.46@ = 8.9
@ = 1.63

Then its all a matter of plugging it into the formula A = [ r²(@-sin@) ]/2

[ 5.46²(1.63 - sin 1.63) ] / 2 = A = 9.416769344 cm² = 9.4 cm² (1dp)

Also note that @ is in radians, not degrees.

 

[atakach99]

mmmmm.... i jsut checked the answer at the back of the book and it says the answer is
9.4 cm squared

 

[tommykins]

mmmmm.... i jsut checked the answer at the back of the book and it says the answer is
9.4 cm squared

Ah, yes it is 9.4, I forgot to turn my calculator into radians (ironic isn't it).

All the calculations are correct however.