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![[Post New]](/templates/default/images/icon_minipost_new.gif) 25 Feb 2007 16:13:28 IST
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A farmer owns a field in the form of a regular hexagon , each side being 40 metres in length . He has a donkey tied by a rope 50 metres long which is fastened to a post in one corner of the field . How many square metres of the field can the donkey graze over ?????
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Umang |
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25 Feb 2007 16:16:53 IST
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It is just calculation of area using the formula of area of a sector of circle.
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25 Feb 2007 16:20:30 IST
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hey ! pls read the question carefully . Its a hexagonand not a circle . Also , length of rope ig greater than its side . If u get the answer , pls post it here !!!
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Umang |
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25 Feb 2007 16:36:55 IST
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Someone pls help !!!!!!!
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Umang |
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25 Feb 2007 16:54:21 IST
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Hi umang, IT's real simple... Area =(area of sector of circle with rad =50 m ) - 2(area of smaller sectors) ; =(1/3)  R 2 - 2(1/6) r 2 ; {where R = 50 m , r = 10 m }
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25 Feb 2007 17:03:01 IST
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Hey vinu ! yes , I got it !!! I was doing it in a different way but couldn't succeed . Its a very easy question ! Thanks !!!!!
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Umang |
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25 Feb 2007 17:23:29 IST
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Hey vinu ! the answer is wrong . This is because the 2 small sectors u considered are not sectors .their length is varying . See ,you hav assumed the part of small sector cutting the hexagon equal to 10 . But infact , it is not 10 . If you see the triangle formed inside the hexagon , sum of two sides is equal to 3rd side , which is not possible (40+10=50) . Pls check and reply !!!!!!
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Umang |
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25 Feb 2007 17:25:51 IST
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if ABCDEF is a hexagon , and A is fixed point , let the big sector cut it at pts P and Q . Just see triangle ABP . AB(40) + BP > AP(50) . So , BP cant be 10
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Umang |
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26 Feb 2007 18:11:20 IST
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Hey vinu ! Pls explain !!!!!
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Umang |
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26 Feb 2007 22:34:16 IST
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Oh yeah, u r right umang; Okay, do it directly then... ABCPRQ Is the area.{ P,Q as defined by u ; R lies on circle of rad 50 m ; B,O,R - collinear.} Area = 2 (  /360) r 2 + 2(1/2)*40*50*Sin  ; {  RBP = , PBA = } use the relations... + = 60 0 ; (40 / Sin ) = (50 / Sin 120 0); u shud get the ans...  |
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27 Feb 2007 12:56:05 IST
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Well Vinu, two days back i read dis question here n tried doin it by da very method you have suggested above, but it turns out dat u get only da value of sin alpha n not da angle itslf, n also, da value is not a well known one, so it becomes really difficult to carry on da calculations further... is there any other method anyone can suggest?
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Aashii, Simply can't study for long |
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28 Feb 2007 22:14:59 IST
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Hey vinu ! I hav got what u r trying to do , but I dont understand the last step . Also , I dont think we'll be able to get the result !!! If u hav calculated , then pls show it here ! Thanks !!!!!!
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Umang |
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28 Feb 2007 23:49:34 IST
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GOOD MAN , GOOD QUESTION (BUT CAN BE SIMPLIFIED)..................right ...........becuse MAIN HOON NAA(KIDDING)............. NOW LOOK . 1)draw the figure. mark P & Q WHEREthe curve touches hexagon..........right....... 2) join AP & AQ............................u will find 2 TRIANGLES(ABP)& AFQ) & 1 SECTOR(PAQ) ..........................right.... 3) USE COSINE LAW TO FIND LENGTH OF PB................. WHICH IS=16(APPROX)=QF) ( as tri ABP similar tri AQF) FIND THE AREA OF ABP & AQF= 2* 1/2 *16*40*sin 120 (using area =1/2*a(PB)*b(AB)*sin120)= 320*(sqrt3)[1.732] = 554.25 .............(1) 4) now setor area = ( 120-2 )/360 * pi * 50 2now can be calculated by using sine rule in ABP............ we get =17.8 sector area = 1837.9...........(2) ad 1+2= 2392.1(answer) I MS SURE............FREEZE IT...................... DON.........
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BELIEVE IN URSELF.....BECAUSE I BELIEVE IN U.............. |
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1 Mar 2007 00:56:24 IST
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Well, don007 seems to hav got de right ans as i hav approximately got de same ..my ans comes to b arnd 2468.65sq m....but d only prob is dat i used a scientific calci for d calculation of a few sine angles..v wont b provided with dat though....
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Fear is useless,
Faith is necessary,
Just believe in urself!! |
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1 Mar 2007 07:15:58 IST
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I think vinu've done the same thing as DON except calculating PB {which is tedious, u get quadratic ,see....}
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Sorry,i ate ur brain!!! |
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