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-4
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0answers
24 views

Intersection of cube and sphere surface area and volume [closed]

Given an axis aligned cube with edge lenth L intersects with a sphere with radius r, with its center (x,y,z) outside of the cube. what is the surface area of the sphere lying inside the cube? what is ...
1
vote
2answers
12 views

finding a point on a surface? the surface is an ellipsoid

I have drawn the cross-sections of the surface $2(x-1)^2 + (y+2)^2 +z^2 = 2$ for the given planes, but am now asked to write down a point which is on the surface. I have no idea how to go about this, ...
0
votes
1answer
19 views

Angle between a line and a plane in a cuboid

I was no good at this kind of stuff at school, probably because of bad spacial awareness. I thought I'd revisit it to see if I've improved! I'm stuck on this question: I dropped a perpendicular ...
-1
votes
1answer
37 views

If you know the side length, how do you find the volume of a dodecahedron and why? [closed]

My dodecahedron has a side length of 1.5. I want to know the formula for the volume and the answer. Also, I want to know why.
6
votes
2answers
65 views

What is the volume of $A'EF-ABD$?

$ABCD-A'B'C'D'$ is a cube with a edge length of $6$. $E$ is the midpoint of $A'B'$ and $F$ is the point on $A'D'$ where $|A'F|=2|D'F|$. The question is: what is the volume of $A'EF-ABD$ ? I ...
0
votes
0answers
8 views

Interception Solid

Could someone draw for me (in $\Bbb R^3$, $x,y,z$ axes) the resultant solid of the interception of $x^2+y^2 \le 1$ and $y^2+z^2 \le 1$? I'm getting a little tired of thinking about the solid but can't ...
2
votes
1answer
32 views

Are knot complements prime 3-manifolds?

Well, that is basically the question. Is the complement of a knot, i.e. an smoothly embedded copy of $S^1$ in $S^3$ a prime $3$-manifold? Here I mean by prime: A connected $3$-manifold $M$ is prime ...
1
vote
0answers
23 views

What is the solid angle at a vertex in a snub cube?

I was able to find or derive an expression for most other Platonic or Archimedean solids, but for the snub cube I was not able to find a value nor find an expression anywhere.
0
votes
0answers
60 views

Finding the length of string wound on a cube.

Consider a cylinder of height $h$ cm and radius $r = \dfrac2π$ cm as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point ...
0
votes
3answers
49 views

Finding vertical spacing between string wound on the cylinder.

Consider a cylinder of height $h$ cm and radius $r = \dfrac2π$ cm as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point ...
1
vote
2answers
31 views

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 ...
1
vote
0answers
52 views

Three balls inside a cone

Given a cone with slant height $4$ and radius $2$. Inside there are three identical balls touching each other and lateral surface of the cone. Two of the balls touch the base. What is maximal radius ...
1
vote
2answers
45 views

How to get projection of ellipsoid onto sphere

I'm trying to get the projection of an ellipsoid onto a sphere. Depicted in the image below, I need the projection of the red ellipsoid onto the unit sphere at the origin. I have tried various ...
1
vote
1answer
36 views

Cross Product of vectors in 7 Dimensions [duplicate]

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?)
0
votes
0answers
6 views

perpendicular on a plane

If the plane $lx+my+nz=p$ where $l^2+m^2+n^2=1$ meets the coordinate axes in X, Y, Z and G is the centroid of the triangle XYZ and if the perpendicular to the plane at G, meets the coordinate planes ...
0
votes
1answer
14 views

Pyramid Surface Area

Square based pyramid has a side length of $220$ (b) and a height of $105.$ Find the surface area. I tried by "doing" Pythagorean theorem $110^2+105^2=s$ then i did the equation for surface area ...
0
votes
0answers
28 views

What is the topology where all the direct distances are equal to $d_1$ and all the cross distances are equal to $d_2$

What is the topology (2D or 3D representation) that corresponds to the following description: We have $K$ pairs of points, where pair $k$ is denoted as $(P_k,Q_k)$. We suppose that the distance ...
0
votes
0answers
38 views

Good book for Solid Analytical Geometry?

So my teacher uses this book, William H McCrea's Analytical Geometry of Three Dimensions, but it's awfully hard and dry. I need something with more exercises and better explanations, but that covers ...
7
votes
4answers
330 views

Concentric Equilateral Triangles

I'm currently researching a particular dynamical system that is very geometric in nature. As part of this, I need to prove the following results (the second obviously implies the first). They are ...
0
votes
1answer
54 views

Find the height of frustum of a cone

The diagram shows a piece of wood which is obtained by cutting off the lower section of a cone. Using PI = 3.142, calculate the value of x. I seriously have no idea on how to find $x$. Any helps ...
0
votes
2answers
85 views

Mapping Coordinates on a Plane Tangent to a Sphere into Cartesian Coordinates in 3D Space

Before we begin, I must ask you to keep the vocabulary at high school level. These variables define the point the plane needs to be tangent to – the center of the circle is at the origin. r - defines ...
0
votes
0answers
17 views

Length of a right triangle's hypoteneuse projected onto a sphere

Please forgive me if this is the wrong kind of question, but I need someone to verify or refute my work. One leg of a triangle has length, $b$ (base), resulting from angle theta swept out by a ray ...
0
votes
0answers
21 views

Figuring out the major axis and minor axis of a 3D ellipse

If a $3d$ ellipse $S=\{(x,y,z)|(x^2)/(2t) + y^2$ $\le 1, z=t, \frac{1}{2} \le t \le 1$}$ The answer book gives the major axis to be $1$, but shouldn't the major axis be $\sqrt{2t}$? as even the ...
1
vote
1answer
67 views

Solid mensuration (circles)

Three circles of different radii are tangent to each other externally. The distance between their centers are $9\ cm$, $8\ cm$, and $11\ cm$. Find the radius of each circle. Find the area in between ...
0
votes
0answers
13 views

Do Meissner bodies which have both rounded edges meeting in a vertex as well as rounded edges surrounding a face minimize volume?

There are known to be two kinds of Meissner bodies constructed from Reuleaux tetrahedra - Meissner body Mv with rounded edges meeting in a vertex, and Meissner body Mf with rounded edges surrounding a ...
6
votes
1answer
109 views

Volume of the intersection of two tetrahedra

First, I am far from a mathematician, and this question may be easy, if that's the case, please don't hesitate to let me know. Suppose I have 2 tetrahedra (2 3D simplex), with known ...
0
votes
4answers
109 views

Problem of axiomatic euclidean geometry

Let the usual five postulates of Euclid been given. Let's take also this postulate: "If two points lies on the same plane, the whole straight line joining the two points lies on that plane". Is it ...
2
votes
1answer
67 views

What do you call 'perpendicular but skew' lines?

For example, the seat tube and rear axle of a bicycle or motorcycle. That is, when viewed from above, the seat tube would appear 'perpendicular' to the rear axle. But in 3d reality, the lines are ...
0
votes
1answer
41 views

On Euclid's definition of similar and equal solid figures.

The Euclid's definition of similar solid figures is Similar solid figures are those contained by similar planes equal in multitude. And the Euclid's definition of equal solid figures is Equal and ...
2
votes
0answers
36 views

Determining solid region from bounds of triple integral

If you have an integral such as: $$\int_0^1\int_0^{2-x^2}\int_0^{2-x}f(x,y,z)dydzdx$$ How can you determine the equation for the solid region represented by the bounds of this triple integral? Does ...
0
votes
0answers
22 views

Sylvester–Gallai theorem in Space

Does this statement true of false? Let $P$ be a set of finite points in space,not all of them are in a plane,and any three points are not a line.Can we always find a plane just pass through three ...
1
vote
2answers
45 views

Proof in a tetrahedron - I added my wrong attempt

please help me solve this problem: There is a tetrahedron (ABCD), where $$ > \angle{ACB}=\angle{ADB}=90^\circ $$ and $$ AC=CD=DB $$ Prove, that $$ AB<2CD $$ My (wrong) attempt: I ...
1
vote
1answer
57 views

Feyman's Triangle? How do you find the area of the inner triangle if the outside triangle is equilateral

If triangle $ABC$ is equilateral,$BD/BC=1/3, CE/CA=1/3,$ and $ AF/AB=1/3$. What is the ratio of the area of triangle? I have problems analyzing this triangle I tried to use phythagorean, heron's ...
0
votes
1answer
215 views

Ratio of an isosceles triangle to its altitude is 3:4. find the measures of the angles

The ratio of an isosceles triangle to its altitude is 3:4. find the measures of the angles of triangle? So, I have the altitude formula where $h$= $\sqrt s^2-(\frac{s}{2})^2$ so I was thinking when I ...
0
votes
3answers
32 views

Find the diameter of the new sphere assuming that the volume of a sphere is proportional to the cube of its diameter

Three spheres of diameters 2,3&4 cm's respectively formed into a single sphere.Find the diameter of the new sphere assuming that the volume of a sphere is proportional to the cube of its diameter ...
0
votes
1answer
27 views

Find the diameter of the new sphere assuming that the volume of a sphere is proportional to the cube of its diameter [duplicate]

Find the diameter of the new sphere assuming that the volume of a sphere is proportional to the cube of its diameter. I know that diameter is equal to the twice of radius. How can you possibly solve ...
1
vote
0answers
25 views

How to derive this parametrization of a solid cone

From Wikipedia: A right circular cone with height $h$ and aperture $2\theta$, whose axis is the $z$ coordinate axis and whose apex is the origin, is described parametrically as $$F(s,t,u) = ...
0
votes
1answer
49 views

Do the $2^n$ hyper-octants of a $n$-sphere always have a $n$-dimensional right angle? Is $\pi/2$ only fundamental in $2$ and $3$ dimensions?

In $2$ dimensions, a $2$-sphere can be divided into $2^2 = 4$ congruent pieces, the $4$ quadrants, each of angle $\pi/2$ radians. In $3$ dimensions, a $3$-sphere can be divided into $2^3 = 8$ ...
2
votes
1answer
183 views

Solid mensuration,Solid Geometry book

Hi I'm an engineering student and i really need your help.....can you please suggest some good books you know regarding Solid mensuration/Solid Geometry good for self studying.
9
votes
2answers
306 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
284 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
441 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
20 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
96 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
31 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
42 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
38 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 = ...
-1
votes
1answer
74 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 ...
2
votes
2answers
162 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
66 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 ...