# How do you show a cone inside of a sphere?

I have a sphere of radius 5 and a cone (i.e. z=√(x^2+y^2)) inside of it. I can show them separately, but I'd like to show them together. I've tried a few tricks with opacity, implicit specifications, show, and range changes, but nothing is giving me a satisfying result.

Really I'd like to show the "ice cream cone" shape by itself, but I'd settle for a cone under a hemisphere right now. Anyone know how I can get this done?

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In what sense were your results not satisfying? – Sjoerd C. de Vries Dec 6 '12 at 6:28
@NasserM.Abbasi it was nothing special really. It was basically just Plot3D[x^2+y^2+z^2=25, {x,-5,5},{y,-5,5}] for the sphere and Plot3D[sqrt(x^2+y^2), {x,-5/sqrt(2),5/sqrt(2)},{y,-5/sqrt(2),5/sqrt(2)} for the cone. When I'd try to put them together with the Show command I'd get a squished hemisphere and a cone higher than the sphere even if I'd specified the z component the way that I'd expect it to come out well (i.e. above the xy-plane and stopping at 5). – BlBl Dec 7 '12 at 5:20
@Sjoerd C. de Vries – BlBl Dec 7 '12 at 5:24

Enjoy it!

Graphics3D[{
{Lighter[Brown], Cone[{{0, 0, 0}, {0, 0, -1}}, .25]},
{Yellow, Sphere[{0, 0, .1}, .25]},
{Pink, Sphere[{.15, 0, .2}, .26]},
{Orange, Sphere[{-.1, 0, .25}, .25]}
}, Boxed -> False]

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Yum yum yum yum... – Yves Klett Dec 6 '12 at 7:52
Thanks for that VLC. I'll fiddle with the code to see if I can just get away with this. – BlBl Dec 7 '12 at 5:25

Something related from a Christmas notebook I wrote last year:

Candle[color_, Pos_] :=
{color, Cylinder[{Pos, Pos + {0, 0, 0.1}}, 0.013],
Black, Thick, Line[{Pos + {0, 0, 0.1}, Pos + {0, 0, 0.12}}],
Yellow, EdgeForm[None], Sphere[Pos + {0, 0, 0.12}, 0.013],
Cone[{Pos + {0, 0, 0.121}, Pos + {0, 0, 0.16}}, 0.0127]}

Graphics3D@Candle[Red, {0, 0, 0}]


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Vanilla, Strawberry and Pistachio, after VLC ...

Graphics3D[{{Lighter[Brown],
Cone[{{0, 0, 0}, {0, 0, -1}}, .25]}, {LightGreen,
Sphere[{0, 0, .1}, .25]}, {Pink,
Sphere[{.15, 0, .23}, .26]}, {LightGray,
Sphere[{-.1, 0, .25}, .23]}}, Boxed -> False,
Lighting -> "Neutral"]


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