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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How many bricks will be needed for the given measurements?

Dimension of garden: Length = 120 metre Breadth = 90 metre Dimension of brick: Length = .25 metre Breadth = .125 metre Thickness= .08 metre Dimension of wall: Height = 2 metre Thickness = .25 metre [P.S. This not a homework rather a mathematical…
Jayed Yeameen
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Octahedrons whose faces are congruent quadrangles

There is a octahedron which the faces are all congruent quadrangles. Let $M$ the set of length of edges of faces of the octahedron. Prove that $|M| \le 3$. Prove that all faces have two edges with equal length which meets at one point. My…
coding1101
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Volume of a trapezoidal prism

A pile of ore has a rectangular base, 60 feet wide and 500 feet long. If the sides of the pile are all inclined 45degrees to the horizontal, and the ore weighs 110 lb. per cu.ft. Find the number of tons of ore in the pile. ( 1ton = 2000 lb). If…
Lyzserg
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to find the slant height of a conical frustum given its top radius, it's lateral surface area and it's common central angle

I've searched high and low for a formula for finding the slant height of a conical frustum given it's top radius, it's lateral surface area and it's common central angle but have come up empty handed. There are lots of formulae out there but none…
David Walden
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Apex of Tetrahedron | AIME 1999

Here's a problem that I'm stuck on:Consider the paper triangle whose vertices are $(0,0), (34,0),$ and $(16,24).$ The vertices of its midpoint triangle are the midpoints of its sides. A triangular pyramid is formed by folding the triangle along the…
TheLeogend
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Does the average height change after we squished the base?

My question is, for an arbitrary surface $z = f(x,y)$, if the base coordinate x and y has experienced some linear transformation. Can I multiply the old calculated average height in Z direction to the new base area in XY to get the new volume?
Zhidong Li
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Prove. The sum of the distances from a random point in a regular tetrahedron to each of its walls = *h*

We have a random point A in a regular tetrahedron. Prove that the sum of the distances from A to each wall is equal to the height of the tetrahedron.
J. Doe
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Volume of a prism

Right rectangular prism has a base with diagonal a and a lateral face with diagonal b. Find the volume of the prism.
J. Doe
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Find the height of a right prism with base-rhombus.

The base of a right prism is a rhombus. Find the height of the prism, if its diagonals are d1 and d2.
J. Doe
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Need help in understanding part b of the question - Cylinder and hemisphere

Please, can anyone tell how the answer is 9.5 for part b? Thank you.
Dinesh Potluru
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If |A×B|=3 , and each of And and B is parallel to the plane YZ , Find A×B A×B is Cross product of vectors

If $|A×B|=3$ , and each of $A$ And and $B$ is parallel to the plane $YZ$ , Find $A×B$ $A×B$ is Cross product of vectors
user373141
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Semi-circle folded into a cone with a circular base

From my 7th-grade math book: The semicircle shown is folded to form a right circular cone so that the arc PQ becomes the circumference of the base. Find the diameter of the base, Let $\text{circumference of cone base}=C$ and…
Soha Farhin Pine
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What is the maximum number of spheres each with radius $1$ cm can be packed in the cuboid?

Acuboid with length $10$ cm width $8$ cm and height $2\pi $ , What is the maximum number of spheres each with radius $1$ cm can be packed in the cuboid ? I searched the web and found a lot of talking about this kind of problems , different…
Medo
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Given the shape below , describe the Solid of revolution obtained by rotating the curve about x axis?

Given the shape below , describe the Solid of revolution obtained by rotating the curve about x axis? Scale is not important I need a visual 3D- graphing for this problem , please !! Is there any website that can help me in familiar…
Medo
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Solid geometry problem tetrahedron

DABC is a tetrahedron and ABC is an equilateral triangle and $AB=BC=CA=2a$ Given that $DA=DB=DC$ and the distance to the plane $ABC$ from $D$ is $3a$ Find the angle between $DA$ and $ABC$. When I was trying to draw a sketch of the tetrahedron…
ranmal fernando
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