Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [solid-geometry]

In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space. (Ref: http://en.m.wikipedia.org/wiki/Solid_geometry)

In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space. Reference: Wikipedia.

Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, cylinders, cones, truncated cones, spheres, and prisms.

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Why does this method to find the surface area of a frustum not work?

I was doing a few problems involving frustums, specifically right circular frustums, and I kept getting the surface area wrong using a certain method that made sense logically. Here is my method: Obviously, a frustum is the result of a cone being…
anirudh30three
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Can dis-similar polyhedral solids have the same surface area to volume ratio?

I am trying to find an efficient way to determine if two polyhedral solids are similar or not. So I am wondering if dis-similar solids that have the same number of faces can have the same surface area to volume ratio? If that is impossible then I…
W.J.
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How to arrange points in three-dimensional space to minimise "repulsion"?

I thought of this while studying Chemical Bonding and the VSEPR theory, where we arrange surrounding atoms around a central atom to minimise repulsion between them. So I wondered how to mathematically go about it (in Chemistry, there are a bunch of…
Righter
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Help with school solid geometry

In the triangular pyramid $MABC$ all side edges equals $1$, $\angle AMB = \angle BMC = 60 ^\circ$, $\angle AMC = 45 ^\circ$. Find: 1) square of the $\triangle ABC$; 2) dihedral angle on the $AB$ edge; 3) $\rho(M, ABC)$. Help me, please. P.S. sorry…
cheremushkin
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How to calculate angles of an object relative to gravity based on rotation

Considering a cube which is along $x,y,z$ axes, $y$ being parallel with gravity, at its "resting" point, $x$ and $z$ will be running at 90 degrees relative to gravity, and $y$ will be $0$ (parallel). If I rotate this cube 30 degrees around the $z$…
Chris A
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Angle between two lines in 3D when three other angles are known.

I came across this while solving some optics related question. Please have a look at the image link. Image So, in the diagram, lines AO and BO lie on the XY plane. I know that $\ \angle AOX=\angle BOX=\theta$, $\angle POX=\phi$ and the angle made by…
Kurious
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Show that sphere passes through 9point circles of faces of a tetrahedron

O is the origin and A, B, C are points (4a,4b,4c),(4b,4c,4a),(4c,4a,4b) show that sphere x^2+y^2+z^2-2(x+y+z)(a+b+c)+8(bc+ca+ab)=0 passes through nine point circles of faces of tetrahedron OABC
Akhil Varma
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Coordinates for vertices of the "silver" rhombohedron.

The "silver" rhombohedron (a.k.a the trigonal trapezohedron) is a three-dimensional object with six faces composed of congruent rhombi. You can see it visualised here. I am interested in replicating the visualisation linked to above in MATLAB, but…
Daniel Pietrobon
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Why does folding a sector yield a flat surface?

We have all folded the two straight parts of a sector together to form a cone, perhaps in elementary school. This cone has a 'flat bottom'. I was asked by a student why it is the case that we have a flat bottom. I thought about it but from a…
Trogdor
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Solid Geometry : Distance of a point to a plane and distance of a point to a line.

$ABCDA'B'C'D'$ is a cube with side $4$, $M$ is the center of the face $A'B'C'D'$ and $H$ is a point on $AC$ such that $AH : HC = 1 : 3.$ a. Find the distance from $B$ to the plane $HMC$ using solid geometry. I got that distance to be…
bob
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name of this shape [3d solid]

what is the name of this 3d solid please? "faces" of 3 and 4 sides. Thanks!
manuelBetancurt
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Determine the angle between two planes

Given vectors $\vec{a}=(3,-2,1),\vec{b}=(1,1,-4)$. Determine the angle between a plane that contains vectors $\vec{a},\vec{b}$ and a plane that contains vectors $\vec{a},\vec{b}+\vec{a}\times \vec{b}$. There is the equation for angle between two…
user300045
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Finding the side lengths of a rectangular prism when you know the diagonal length and 3 angles

I am trying to find the side lengths of a rectangular prism. The diagonal length is 1 and I know the angles connecting the diagonal corners of each side. Here is a diagram: My question is: remembering that the sides x, y, and z are not equal, what…
Matt Spoon
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What is the minimum information needed to determine a line in 3D?

Motivation: A Line in $\Bbb R^2$ Any line can be uniquely determined by two points. In $\Bbb R^2$, a point is uniquely determined by two values (its $x$ and $y$ coordinates). Hence, to uniquely determine a line in $\Bbb R^2$ requires at most four…
Tim Pederick
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why aren't prisms archimedian solids?

I don't understand which part of the definition of an archimedian solid excludes prisms from being one. each vertex of a prism has the same polygons around it (4,4,n for a n-gonal prism), and also each vertex is symmetrical to every other vertex,…
stanley dodds
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