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[SPAM] RE: [obm-l] esfera no cone
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--_8e364f82-9f67-4b2d-bf80-89740f91c617_
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Liga do centro da esfera ao lado do cone, at=E9 o ponto de tang=EAncia,form=
ando assim dois triangulos ret=E2ngulos semelhantes.
=20
R/6 =3D8-R/10 , da=ED teremos que R=3D3.
=20
Espero ter ajudado.
=20
Cl=E1udio Thor
=20
=20
> Date: Thu, 29 Nov 2007 22:39:01 -0300> From: emanuelvalente@xxxxxxxxx> To=
: obm-l@xxxxxxxxxxxxxx> Subject: Re: [obm-l] esfera no cone> > Ney Falcao w=
rote:> > Como seria possivel calcular a =E1rea pedida no problema abaixo se=
m > > conhecer o raio da esfera?> > > > /Calcule o volume exterior a uma es=
fera e interior a um cone de raio > > da base igual a 6 e altura 8, sendo a=
esfera inscrita no cone/.> > > > Obrigado> > Ney> Ol=E1 Senhores, como v=
=E3o?> > Seguinte, fiz um esbo=E7o do problema no paint. Tamb=E9m embuti a =
rela=E7=E3o da > semelhan=E7a de tri=E2ngulos:> http://epaduel.org/tmp/obm-=
29112007.jpg> > Dados do problema:> H =3D x + r =3D> x =3D 8 -r (I)> > Da s=
emelhan=E7a de tri=E2ngulos:> x/r =3D a/R (II)> > De I em II:> (8-r)/r =3D =
a/6 =3D> a =3D 6(8-r)/r (III)> > Aplicando pit=E1goras no tri=E2ngulo ret=
=E2ngulo maior:> > a^2 =3D h^2 + R^2 =3D> a^2 =3D 64 + 36 (IV)> > De (III) =
em (IV)> > [6(8-r)]^2 =3D 100r^2> r^2 +9r -36 =3D 0> x=B4 =3D 12 nao conv=
=E9m (r>R)> x=B4=B4 =3D -3, logo r =3D 3> > Calculando os volumes:> > Vesf =
=3D (4/3)pi*r^3 =3D> (4/3)*pi*3^3 =3D> 36pi> Vcone =3D (1/3)*pi*(R^2)*H =3D=
> (1/3)*pi*(6^2)*8 =3D > 96> > Respostas: Vesfera =3D 36pi> Vext =3D 96pi -=
16pi =3D 60pi> > > Se estiver errado, por favor,me corrijam!> > Abra=E7os a=
todos,> > Emanuel Valente> > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D> Instru=E7=F5es para entrar na lista, sair d=
a lista e usar a lista em> http://www.mat.puc-rio.br/~obmlistas/obm-l.html>=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
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_________________________________________________________________
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Liga do centro da esfera ao lado do cone, at=E9 o ponto de tang=EAncia,form=
ando assim dois triangulos ret=E2ngulos semelhantes.<BR>
<BR>
R/6 =3D8-R/10 , da=ED teremos que R=3D3.<BR>
<BR>
Espero ter ajudado.<BR>
<BR>
Cl=E1udio Thor<BR>
<BR>
<BR>
<BR><BR>> Date: Thu, 29 Nov 2007 22:39:01 -0300<BR>> From: emanuelval=
ente@xxxxxxxxx<BR>> To: obm-l@xxxxxxxxxxxxxx<BR>> Subject: Re: [obm-l=
] esfera no cone<BR>> <BR>> Ney Falcao wrote:<BR>> > Como seria=
possivel calcular a =E1rea pedida no problema abaixo sem <BR>> > con=
hecer o raio da esfera?<BR>> > <BR>> > /Calcule o volume exteri=
or a uma esfera e interior a um cone de raio <BR>> > da base igual a =
6 e altura 8, sendo a esfera inscrita no cone/.<BR>> > <BR>> > =
Obrigado<BR>> > Ney<BR>> Ol=E1 Senhores, como v=E3o?<BR>> <BR>&=
gt; Seguinte, fiz um esbo=E7o do problema no paint. Tamb=E9m embuti a rela=
=E7=E3o da <BR>> semelhan=E7a de tri=E2ngulos:<BR>> http://epaduel.or=
g/tmp/obm-29112007.jpg<BR>> <BR>> Dados do problema:<BR>> H =3D x =
+ r =3D> x =3D 8 -r (I)<BR>> <BR>> Da semelhan=E7a de tri=E2ngulos=
:<BR>> x/r =3D a/R (II)<BR>> <BR>> De I em II:<BR>> (8-r)/r =3D=
a/6 =3D> a =3D 6(8-r)/r (III)<BR>> <BR>> Aplicando pit=E1goras no=
tri=E2ngulo ret=E2ngulo maior:<BR>> <BR>> a^2 =3D h^2 + R^2 =3D> =
a^2 =3D 64 + 36 (IV)<BR>> <BR>> De (III) em (IV)<BR>> <BR>> [6(=
8-r)]^2 =3D 100r^2<BR>> r^2 +9r -36 =3D 0<BR>> x=B4 =3D 12 nao conv=
=E9m (r>R)<BR>> x=B4=B4 =3D -3, logo r =3D 3<BR>> <BR>> Calcula=
ndo os volumes:<BR>> <BR>> Vesf =3D (4/3)pi*r^3 =3D> (4/3)*pi*3^3 =
=3D> 36pi<BR>> Vcone =3D (1/3)*pi*(R^2)*H =3D> (1/3)*pi*(6^2)*8 =
=3D > 96<BR>> <BR>> Respostas: Vesfera =3D 36pi<BR>> Vext =3D 9=
6pi -16pi =3D 60pi<BR>> <BR>> <BR>> Se estiver errado, por favor,m=
e corrijam!<BR>> <BR>> Abra=E7os a todos,<BR>> <BR>> Emanuel Va=
lente<BR>> <BR>> <BR>> <BR>> <BR>> =3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D<BR>> Instru=E7=F5es para e=
ntrar na lista, sair da lista e usar a lista em<BR>> http://www.mat.puc-=
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=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D<BR><BR><br /><hr />Conhe=E7a o Windows Li=
ve Spaces, o site de relacionamentos do Messenger! <a href=3D'http://spaces=
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