Trigonometry problem
in [Math]
|
Prev: deriving speed of light out of pure math as pseudosphere nested inside sphere Chapt 19 #215; ATOM TOTALITY
Next: How to investigate online casino RNG
From: Ludovicus on 8 Jul 2010 11:03 On 8 jul, 01:59, Fred Nurk <albert.xtheunkno...(a)gmail.com> wrote: > A sphere of radius length 8 cm rests on the top of a hollow inverted cone > of height 15 cm whose vertical angle is 60 degrees. Find the height of > the centre of the sphere above the vertex of the cone. > > Where is the vertical angle located on a cone? > > TIA, > Fred It is impossile that a sphere of 16 cms of diameter can rest on the top of that cone. Because the diameter on the top of a cone of 60 degrees at 15 cms is 17.32 cms. The height must be an unknown quantity , not 15.
From: Francois Grieu on 8 Jul 2010 13:10 Le 08/07/2010 17:03, Ludovicus a écrit : > On 8 jul, 01:59, Fred Nurk <albert.xtheunkno...(a)gmail.com> wrote: >> A sphere of radius length 8 cm rests on the top of a hollow inverted cone >> of height 15 cm whose vertical angle is 60 degrees. Find the height of >> the centre of the sphere above the vertex of the cone. >> >> Where is the vertical angle located on a cone? > > It is impossile that a sphere of 16 cms of diameter > can rest on the top of that cone. Not fully on top, but still that sounds on top to me. > Because the diameter on the top of a cone of 60 degrees > at 15 cms is 17.32 cms. Yes. > The height must be an unknown quantity, not 15. "height 15 cm" allow to compute an answer; it would be the same for "height 16 cm", but not for "height 5 cm". Francois Grieu
From: Ludovicus on 8 Jul 2010 15:19 On 8 jul, 13:10, Francois Grieu <fgr...(a)gmail.com> wrote: > Le 08/07/2010 17:03, Ludovicus a écrit : > > > On 8 jul, 01:59, Fred Nurk <albert.xtheunkno...(a)gmail.com> wrote: > >> A sphere of radius length 8 cm rests on the top of a hollow inverted cone > >> of height 15 cm whose vertical angle is 60 degrees. Find the height of > >> the centre of the sphere above the vertex of the cone. > > >> Where is the vertical angle located on a cone? > > > It is impossile that a sphere of 16 cms of diameter > > can rest on the top of that cone. > > Not fully on top, but still that sounds on top to me. > > > Because the diameter on the top of a cone of 60 degrees > > at 15 cms is 17.32 cms. > > Yes. > > > The height must be an unknown quantity, not 15. > > "height 15 cm" allow to compute an answer; it would be > the same for "height 16 cm", but not for "height 5 cm". > > Francois Grieu It's not necessary the height nor the diameter to compute the answer. The answer is: In a cone of 6o degrees the center of a sphere in contact with the inner surface, is at one diameter from the vertex of cone.
From: Francois Grieu on 8 Jul 2010 16:44 Le 08/07/2010 21:19, Ludovicus a �crit : > On 8 jul, 13:10, Francois Grieu<fgr...(a)gmail.com> wrote: >> Le 08/07/2010 17:03, Ludovicus a �crit : >> >>> On 8 jul, 01:59, Fred Nurk<albert.xtheunkno...(a)gmail.com> wrote: >>>> A sphere of radius length 8 cm rests on the top of a hollow inverted cone >>>> of height 15 cm whose vertical angle is 60 degrees. Find the height of >>>> the centre of the sphere above the vertex of the cone. >> >>>> Where is the vertical angle located on a cone? >> >>> It is impossile that a sphere of 16 cms of diameter >>> can rest on the top of that cone. >> >> Not fully on top, but still that sounds on top to me. >> >>> Because the diameter on the top of a cone of 60 degrees >>> at 15 cms is 17.32 cms. >> >> Yes. >> >>> The height must be an unknown quantity, not 15. >> >> "height 15 cm" allow to compute an answer; it would be >> the same for "height 16 cm", but not for "height 5 cm". >> >> Francois Grieu > > It's not necessary the height nor the diameter to compute the answer. > The answer is: > In a cone of 6o degrees the center of a sphere in contact with the > inner surface, is at one diameter from the vertex of cone. That's true if the height of the cone is at least 3^(1/2) times the radius of the sphere; Below that limit, the contact circle between the sphere and the cone changes, and the sphere lowers. Francois Grieu [reposted with correction]
From: Rob Johnson on 8 Jul 2010 17:52
In article <4c3638ac$0$10461$426a74cc(a)news.free.fr>, Francois Grieu <fgrieu(a)gmail.com> wrote: >Le 08/07/2010 21:19, Ludovicus a �crit : >> On 8 jul, 13:10, Francois Grieu<fgr...(a)gmail.com> wrote: >>> Le 08/07/2010 17:03, Ludovicus a �crit : >>> >>>> On 8 jul, 01:59, Fred Nurk<albert.xtheunkno...(a)gmail.com> wrote: >>>>> A sphere of radius length 8 cm rests on the top of a hollow inverted cone >>>>> of height 15 cm whose vertical angle is 60 degrees. Find the height of >>>>> the centre of the sphere above the vertex of the cone. >>> >>>>> Where is the vertical angle located on a cone? >>> >>>> It is impossile that a sphere of 16 cms of diameter >>>> can rest on the top of that cone. >>> >>> Not fully on top, but still that sounds on top to me. >>> >>>> Because the diameter on the top of a cone of 60 degrees >>>> at 15 cms is 17.32 cms. >>> >>> Yes. >>> >>>> The height must be an unknown quantity, not 15. >>> >>> "height 15 cm" allow to compute an answer; it would be >>> the same for "height 16 cm", but not for "height 5 cm". >>> >>> Francois Grieu >> >> It's not necessary the height nor the diameter to compute the answer. >> The answer is: >> In a cone of 6o degrees the center of a sphere in contact with the >> inner surface, is at one diameter from the vertex of cone. > >That's true if the height of the cone is at least 3^(1/2) times >the radius of the sphere; >Below that limit, the contact circle between the sphere and the >cone changes, and the sphere lowers. If, by "height of the cone", you mean the distance from the base of the cone to its vertex (this is the usual meaning, and is the "h" used in the formula V = 1/3 B h), then the height of the cone must be 3/2 the radius of the sphere. In the extreme case, the radius of the base of the cone is sqrt(3)/2 times the radius of the sphere, and the height of a 60 degree cone is sqrt(3) times the radius of the base of the cone. Thus, the height of the cone must be at least 3/2 the radius of the sphere. Rob Johnson <rob(a)trash.whim.org> take out the trash before replying to view any ASCII art, display article in a monospaced font |