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8
votes
2answers
272 views

How to show that five points in ℝ³ are cospherical?

There are many conditions equivalent to the cocircularity of four points on a plane, however i could not find any such lists for the three-dimensional analog. When do five points in three-dimensional ...
0
votes
2answers
36 views

Volume, Lateral Area, and Surface Area of an Elliptic Conical Frustum

What are the formulae for the volume, surface area, and lateral area (i.e. the surface area without the bases) for the above illustrated elliptic conical frustum? I think I've got the volume figured ...
2
votes
1answer
34 views

Surface area of quarter of a Sphere

A quarter sphere with a radius of $10 \text{ units}$. Please help, also remember the sides. I used the normal formula of the total surface area of a sphere and divided it by $4$, then added half the ...
0
votes
0answers
15 views

How To Find a Set of Points Farthest Apart Within 3D Solid

I am trying to find out a method to solve the following problem: There are two parameters: 1) There is a solid 3D region plotted in a cartesian coordinate system. 2) There is a number of points that ...
1
vote
2answers
50 views

Proving that the volume of a pyramid is one-third that of its corresponding prism.

Is there any way to prove that for any isosceles triangle, the volume of a solid created when that triangle is projected to a point determining the height above the angle opposite the hypotenuse is ...
1
vote
0answers
25 views

Parametrization of a bounded solid.

So, I have a solid bounded by $z=\sqrt{x^2+y^2}, z=\sqrt{1-x^2-y^2}, z=2$ I had to parametrize it using spherical coordinates so I used $$\begin{cases} x(\rho, \theta, ...
1
vote
0answers
30 views

Determining diameter of strands of twisted rope

Twisted ropes are made by taking 3 strands of smaller rope and twisting them together tightly, by coiling the strands in the same direction, as opposed to braided rope, which requires strands to be ...
0
votes
0answers
21 views

Volume of Solid of Revolution

This problem is giving me some trouble: The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. x = (y − 5)^2, x = 4; ...
-1
votes
1answer
45 views

Volume of Cavity between intersecting multiple Spheres

I want find an equation for this problem: Problem Statement:: I have different size sphere, for example say $R_1$ for Red balls and $R_{2}$ for white Balls, overlapping each other. 1.) I want to ...
1
vote
2answers
70 views

Why isn't the volume formula for a cone $\pi r^2h$?

So I understand that the volume formula of a cone is: $\frac{1}{3}\pi r^2h$, and when I read about how to derive this formula, it makes sense to me. Funny thing is, I'm stuck on why it ISN'T $\pi ...
2
votes
0answers
41 views

Inscribed spheres in irregular tetrahedra

Let $ABCD$ be an irregular tetrahedron, and let $K$ be the center of its inscribed sphere. Let $M$ be the center of the inscribed sphere of $KBCD$. Are $A$, $M$, $K$ necessarily collinear? I have ...
0
votes
0answers
34 views

Numerical Integration Over Two Regions of an Ellipsoid

I would like to perform a numerical integration over the surface of an ellipsoid $D$. The domain must be split in two by a plane intersecting the ellipsoid (the intersection is arbitrary), so that we ...
0
votes
1answer
39 views

Pyramid problem - find the height of the pyramid by given edges and a side from the base

The base of a pyramid is a right triangle with the longest side = 12cm. All non base edges are also equal to 12cm. And how can I find the height of the pyramid?
3
votes
1answer
40 views

A cross-section of a pyramid

Show that for $n\ge 5$, a cross-section of a pyramid whose base is a regular $n$-gon cannot be a regular $(n + 1)$-gon. This is a repost from this. Can someone help me? Thanks in advance.
1
vote
0answers
17 views

Computing Solid Geometry from Surfaces - CAD

I'm an engineer and I recently took a course at my local university about CAD curves and surfaces. I understand how NURBS surfaces work and how to generate the complex surfaces that models consist of. ...
0
votes
1answer
37 views

Intersection of a plane and a surface of revolution

I'm am stuck on the following problem: I have the equation of a curve in the plane $(x,z)$: $z=f(x)$. I build a surface of revolution in the space rotating this curve around the $z$ axis. I need to ...
2
votes
1answer
42 views

Regular pyramid, centre of circumscribed ball=centre of inscribed ball

Prove that if the sum of plane angles in the vertex of a regular pyramid equals $180 ^{\circ}$, then in this pyramid the centers of the inscribed and circumscribed balls are equal. Could you help me ...
2
votes
1answer
40 views

Find radius of sphere

Imagine eight spheres of radius 1 that are at $(\pm1,\pm1,\pm1)$. Place sphere A with its center at the origin externally tangent to all of the other spheres. Then place sphere B externally tangent to ...
4
votes
2answers
89 views

Why are polyhedra related to the prime numbers 2, 3 and 5, but not to the prime number 7?

Just take a quick glance at all the numbers in these Wikipedia pages on polyhedra: http://en.wikipedia.org/wiki/Platonic_solid http://en.wikipedia.org/wiki/Archimedean_solid ...
0
votes
0answers
24 views

volume swept by a triangle

I have two triangles defined in space, say $(a,b,c)$ and $(a',b',c')$, where the second one is the outcome of a linear transform of the first. The lines connecting corresponding vertices ($(a-a')$, ...
1
vote
1answer
57 views

Solid Trigonometry

V ABCD is a pyramid with the vertex V situated perpendicularly above the centre of the square base ABCD. If $\theta$ is the angle between the edge VA and the base, and $\phi$ is the angle between the ...
6
votes
1answer
85 views

Platonic solids and charged particles

It is known that there are five Platonic solids: If, lets say, there are 4 particles with the same electricity charge and whose movement is constrained to be on a sphere, resulting forces will ...
0
votes
0answers
115 views

Generate X, Y, Z coordinates of 3D triangular prism with Edge Rounding

I'm trying to create an interactive 3D visualization with Python and Mayavi for inputs to an analysis program. The program accepts certain primitive shapes which it combines (constructive solid ...
0
votes
0answers
16 views

What is the distance between plane ACH and BEG from this following cube?

Given: cube ABCD.EFGH with length of its edge is r cm. What is the distance between plane ACH and BEG? Here is my attempted drawing: http://i57.tinypic.com/wgtc1.png From this picture, I take a ...
1
vote
1answer
82 views

How can the tension force be computed to test if a shape is moving or not?

Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ...
3
votes
1answer
87 views

How to compute force on joints of a 3D structure of balls connected by rods?

Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ...
0
votes
0answers
42 views

Question about relationship between line and plane in solid geometry?

Given: Cube ABCD.EFGH, with P and Q as midpoints of CG and BF respectively. What is the relationship between: a. EP and plane ABCD b. AC and plane EQPH My attempt: a. Since EP at plane ACGE ...
0
votes
1answer
70 views

Triangle inside a cylinder, surface times circumference - hard to visulize question

The surface of the triangle is $X$ and the circumfrence of the base of the cylinder is $Y$. What is the volume of the cylinder ? The answer is $XY$ but why ? If you'll take the ...
2
votes
1answer
185 views

Solids of Revolution - Negative volume?

So I'm to find the volume of the solid formed by the area trapped between $y = x$ and $y = \sqrt{x}$, rotated about $y = 1$ The two curves cross at y = 0 and y = 1 so they will be the upper/lower ...
-1
votes
1answer
38 views

locus sections and circles--symmetry

A. Let L = {(x,y,z)|the distance from (x,y,z) to the y-axis is 6}. Describe what shape L is. So far, I have that it's a circle, but I'm not sure how to describe it fully. Would it be a circle that ...
1
vote
2answers
151 views

Use cylinder's formula for frustum (conical frustum)

I know that frustum(conical) has a formula for its volume,i.e. $\frac1 3\pi h(r^2+R^2+rR)$, but why can't we place the average of two radii into cylinder's formula: $\pi(\frac{r+R}2)^2(h)$? I need ...
0
votes
0answers
81 views

Difference between polyhedral, CSG and B-rep

I am working on the 3D object modeling project. I found objects can be represented in the form of Polyhedrol model, CSG (Constructive Solid Geometry) model, and as well as B-Rep (Boundary ...
0
votes
1answer
122 views

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 ...
0
votes
0answers
112 views

Lattice orthogonal polyhedra face-area sequences: Golyhedra?

Let $P$ be a polyhedron, all of whose vertices are at points of $\mathbb{Z}^3$, all of whose edges are parallel to an axis, with every face simply connected, and the surface topologically a sphere. ...
6
votes
1answer
156 views

Sum of radii of exspheres

I am interested in finding some results for tetrahedron that would be analoguous to known results for triangle. In triangle with circumradius R and inradius r, if we consider the excircles $r_i$, then ...
0
votes
1answer
117 views

Ellipse Tangents in 3D

I know that we can find the tangent of the ellipse in 2D by taking the derivative of the equation defining the ellipse. But I'm little bit confused about finding the ellipse tangent in 3D. Where the ...
0
votes
0answers
37 views

Compute the volume of a solid

I've solved this exercise and my answer contradicts the one in the back of the book. It might be a misprint but I need to be sure. The book is Apostol's Calculus vol. 1. The book says $16\sqrt3/3$, my ...
0
votes
1answer
49 views

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 ...
0
votes
2answers
52 views

Point of tangency between plane and sphere

How can one find the point of tangency between a plane and a sphere in $\mathbb{R}^3$? The equations of the plane and the sphere are $x + y + z - 5 = 0$ and $(x-1)^2 + (y-2)^2 + (z+1)^2 = 3$ ...
1
vote
1answer
77 views

Find the area of the Grayed triangle Given the following Figure

Can you help me find the area of the gray triangle in the given figure. I'm having a hard time finding the base value of the triangle, I've managed to find the sides for the big triangle but not ...
0
votes
1answer
372 views

Line Drawing Using Bresenham Algorithm

Indicate which raster locations would be chosen by Bersenham’s algorithm when scan converting a line from screen co-ordinates (1,1) to (8,5). First the straight values (initial values) must be found ...
0
votes
1answer
103 views

vectors in 3D space and Right-Hand Rule

Suppose we have three vectors in 3D space. My questions are: How we check if these vectors are satisfy the right-hand rule or not. I know that it's possible to make the three vectors satisfy the ...
2
votes
3answers
96 views

Generalization of angle bisector to tetrahedron

Let $I$ be the center of the inscribed sphere of a tetrahedron $ABCD$ and let $I_A$ be the length of the line passing through $I$ from the vertex $A$ to the opposite face. I am looking for a formula ...
2
votes
0answers
21 views

The exact type of my 3d model

I have reconstructed vertical features (hole like objects lie on a vertical face) lie on two connected faces. To understand the situation, I say I have 2 walls with many windows and doors on ...
0
votes
1answer
83 views

Perspective projection onto y/z plane?

On wikipedia there is an article on 3d perspective projection onto the x/y plane. http://en.wikipedia.org/wiki/3D_projection#Perspective_projection How do I project onto the y/z plane? If i have a ...
1
vote
1answer
106 views

Icosahedron and dual dodecahedron coordinates and rotations

I'm trying to build a 20 sided die in Actionscript 3, like one in the picture. I figure the best way would be to make it out of 20 equilateral triangles rotated in 3D space. The vertices of the ...
1
vote
1answer
22 views

calculate size of faces to have similar volume of platonic solids

I need to build some prototype physical shapes of the 5 platonic solids. But the problem is that I want to make them all about the same size, so how to calculate how big should the faces of my ...
2
votes
1answer
45 views

what will be the angle at the centre?

Taken a tetrahedron of same edges, a point is taken inside it which is equidistant from all $4$ vertices, i.e if a sphere is made taking it as a centre, all the vertices will be on the sphere, now ...
2
votes
1answer
125 views

Disk and washer problem

I need to find the volume of the solid obtained by rotating the region bounded by the following functions: $xy = 1, y = 0, x = 1, x = 2;$ about $x = -1$ I think the outer radius of the washer is ...
5
votes
3answers
136 views

Which solids are characterized by their orthographic projections?

If I know the orthographic projections of a given solid in Euclidean 3-space onto the $xy$, $xz$ and $yz$ planes, under which circumstances can I reconstruct the solid based on that information alone? ...