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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Cross Product of vectors in 7 Dimensions

While reading a geometry book I came across something like....... Cross Product is possible only in 3 Dimension system and 7 Dimension system. Why?(or How?)
harshal naik
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Shape/volume of this solid (don't know the name)

Here is the construction of the solid. Take an ellipse, make a copy of it, and put it on top of the original ellipse. Now turn the top ellipse by $90^\circ$ (quarter turn). Glue the two boundaries. I would like the height, volume, and the equation…
abel
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Angles in a Prism Question

This is a problem that I was set by my physics teacher but really seems to be more of a maths problem than a physics one. I have read the guidelines for homework questions and I think I've met all the criteria, I have tried very hard to solve this…
Ben Elgar
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How will I get the volume and surface area of the sphere?

If a rectangular solid have edges, 4 cm, 5 cm and 7 cm, is inscribed in a sphere. How will I get the volume and surface area of the sphere? Do I need to get the volume of the rectangular solid and use it to get the radius of the sphere?
user114811
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Intersected cone, a practical problem

This is the maths representation of a problem which I have from the practice. We have an interested cone with a diameter of the base $d$, height $h$ and the angle $\alpha$ as shown on the drawing. A plane $\gamma$ has been created which passes…
user123949
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perpendicular lines through $F$ project to perpendicular lines

Let $C(0,0,\sqrt{2})$ and $F(0,\sqrt{2},0)$ be two points in $\Bbb R^3$. $AF,BF$ are arbitrary perpendicular lines through $F$ on the plane $y=\sqrt{2}$. These lines project to the lines $DF,EF$ under the perspective projection centered at $C$ onto…
hbghlyj
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cross-section a regular quadrangular pyramid

A regular quadrangular pyramid has a regular pentagon cross-section and the side length of the regular pentagon is known to be $a$. How to find the volume of the pyramid? Is it possible to find the volume of the pyramid? If yes, how to do it?
piteer
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On the diagram $M$ and $P$ are the midpoints of the edges $BC$ and $AB$ of the regular triangular prism $ABCA_1B_1C_1$

On the diagram $M$ and $P$ are the midpoints of the edges $BC$ and $AB$ of the regular triangular prism $ABCA_1B_1C_1$. Which of the following lines is perpendicular to the plane $(BCC_1B_1):$ $AB;\quad PM;\quad A_1M;\quad PC_1?$ I am not really…
yinivem462
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Prove that there is no convex polyhedron

Prove that there is no convex polyhedron with exactly $7$ edges Solution: We show first that for any polyhedron we have $2E \geq 3F$ and $2E \geq 3V$. The faces of the polyhedron are polygons, each bounded by a number of sides. Along each edge…
Lambert macuse
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Fraction of a Cubical volume

There are a lot of cube cutting problems in different texts. This one is an original thought, and actually I have been able to solve it too. But the answer I am getting, is a bit hard to accept from actual shape of solid. Want to validate my answer…
Rupen Kohli
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"Pyramid Theorem" about sine product and cosine substraction

Let point $A(\vec{a}), B(\vec{b}), C(\vec{c}), D(\vec{b}\times \vec{c})$, then by using Vector Triple Product Expansion, I got the following equality: $$ \vert \sin\angle AOD \sin\angle BOC \vert=\vert \cos \angle AOC - \cos \angle AOB…
yunoa7
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producing tetrahedra within a cube

A common math problem involves dividing a cube into regular and irregular tetrahedra, where the points of the cube must also be the points of the tetrahedra. A problem I'm working on seems to be going the other way, i.e., "How many unique ways are…
ridthyself
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Calculate the volume of the solid limited by surfaces

Calculate the volume of the body limited by surfaces: $$ z = 0\\ z = 8-2x-y\\ x^{2} +y^{2} = 4 $$ Have no idea how do it.
KanekiSenpai
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Helical cross-section as result of lathe/milling operation (cylinder intersection)

I suspect a simple wooden toy "lead screw" was made by advancing a cylindrical rotary cutting tool ( Cylindrical End Mill Cutter) along the surface of the rotating wooden dowel (base cylinder), resulting in a helical cut (the axes of the cylinders…
handle
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I have to work with Bisector planes. Can u pls help me?

The points are A (1.0, -1) B (2.3.1) C (0.2, -3) Determine point P that’s from the same distance from A, B and C and at a distance √5 from the plane ABC. ![So this is how I solved it , but I have to do something with Bisector planes)…
user755662
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