What is Pyramid: Definition and 106 Discussions

A pyramid (from Greek: πυραμίς pyramís) is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilateral, or of any polygon shape. As such, a pyramid has at least three outer triangular surfaces (at least four faces including the base). The square pyramid, with a square base and four triangular outer surfaces, is a common version.
A pyramid's design, with the majority of the weight closer to the ground, and with the pyramidion at the apex, means that less material higher up on the pyramid will be pushing down from above. This distribution of weight allowed early civilizations to create stable monumental structures.
Civilizations in many parts of the world have built pyramids. The largest pyramid by volume is the Great Pyramid of Cholula, in the Mexican state of Puebla. For thousands of years, the largest structures on Earth were pyramids—first the Red Pyramid in the Dashur Necropolis and then the Great Pyramid of Khufu, both in Egypt—the latter is the only one of the Seven Wonders of the Ancient World still remaining.

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  1. S

    Finding length in regular pyramid

    Homework Statement Regular pyramid T.ABCD has square base with side 1 cm. N is the mid-point of AB. Find the length of TN Homework Equations not sure The Attempt at a Solution No information given about the height of the pyramid and the length of the slant-edge, such as TA, so how...
  2. Psinter

    What am I doing wrong in finding the volume of a square based pyramid

    1. I need to find the volume of a square based pyramid which one side of its base is 756ft. Its height is 481ft and the material density is 150lb/ft^3It has to be using calculus. 2. Homework Equations : I know that the formula would be 1/3*(b^2*h), but I need to use calculus to reach that...
  3. S

    Solving for Side Length of Right Pyramid with Height/Volume

    Homework Statement Basically the volume of the pyramid is 554.9 and its height is 15.1. I know that the forumla to find the volume of a pyramid is V=1/3lwh but I'm too dumb to figure out how to switch it around to make it work. The Attempt at a Solution I don't even know where to start!
  4. J

    Why we not get attracted by pyramid ?

    why we not get attracted by pyramid ?? pyramid have much mass than us than why we are not attracted by them?
  5. C

    Solve Triangle Pyramid Volume: V=72cm3, h=12cm

    Homework Statement The volume of a pyramid can be evaluated by using the equation V=1/3*A*h where h is the height of the pyramid and A is the area of the base of the pyramid. The problem is to design such a triangular pyramid where the volume is V = 72 cm3 and the height is h = 12 cm. The...
  6. M

    What is the volume of water in an inverted square pyramid with given dimensions?

    Homework Statement An inverted square pyramid has a height equal to 8m and a top edge equal to 3m. Initially, it contains water to a depth of 5m. What is the initial volume of water in the tank? Homework Equations volume=1/3bh where b is e2, as area of square base. The...
  7. J

    Newtonian Gravity involving spheres in a trigonal pyramid

    Homework Statement In deep space, three spherical masses are held in fixed positions (by rods light compared to the masses) at three corners of a square of side length sqrt(18) m as shown. The masses of the three spheres are m1 = m3 = 1.76×10^9 kg, and m2 = 2.75×10^9 kg. A relatively small...
  8. G

    Volume of a Frustrum of a Pyramid

    Homework Statement Find the volume, using only the variables a, b, and h in your answer. A frustum of a pyramid with square base of side b, square top of side a, and height h: Homework Equations Area = length*width. Length of side S = ?? The Attempt at a Solution I...
  9. H

    Moment of Inertia of square based pyramid?

    Homework Statement A regular square pyramid (base length a, height b) is spun about its axis of symmetry z. Calculate its moment of inertia about the z axis Homework Equations volume of pyramid centre of mass The Attempt at a Solution have found volume and centre of mass. I know...
  10. R

    Why isn't the volume of a pyramid Bh/2?

    Hey, so I guess my question is as follows. I've got a problem picturing a pyramid only being Bh/3 and not Bh/2. I've looked at the proof why it is so, and it seems reasonable when looking at it, BUT if I imagine a cone vs. a cylinder sliced with vertical rather than horizontal cuts I'm lost...
  11. A

    Volume of the frustum of a pyramid

    Homework Statement Find the volume of the frustum of a pyramid with square base of side b, square top of side a, and height h. What happens if a = b ? If a = 0 ? Homework Equations None The Attempt at a Solution I know that i have to integrate from 0 to H. I make a generic...
  12. B

    Volume of Frustum Pyramid: 19800.44 ft^3Calculate Volume of Frustum Pyramid

    I had a similar question in the "engineering systems and design" category but didn't get any replies so hear is the simple version involving only the math. Basically I just need to see if I am using the correct formula to the calculate the volume of a frustum pyramid. However the bottom of...
  13. B

    Frustum Pyramid Volume to Design Oil Containment System

    I have attached a word document showing an image and some typed out simple calculations. I am working on an oil containment system for a new building my employer is going to be building soon. Its pretty simple in the middle of the floor we put a catch basin with a 24"x24" grate. This catch...
  14. M

    Allowable error in elevation angle in pyramid of giza

    Homework Statement the base of the great pyramid giza is a square that is 230m on each side. use differentials to estimate the allowable error in the elevation angle that will ensure that the error in calculating the height is at most +,- 5m. phi is the elevation angle of the pyramid. h=...
  15. T

    Using integrals to prove volume of a pyramid

    the first question i have is if i set it up the iteration right. The I've simplified to one quarter of the pyramid, so the value c is actually 1/2 the base of the whole pyramid. and h is the height of the pyramid. (the pinnacle of the pyramid is along the z axis) 0\leq z\leq -\frac{h}{c}x+h...
  16. J

    Integrating for volume of a hexagonal pyramid

    Homework Statement A) Find the volume of a truncated pyramid with a regular hexagonal base. perimeter of bottom = 1.2 km perimeter of top = 480 m height = 200m B) If density = 1500 kg/m^3 how much work was done in construction? Homework Equations The Attempt at a Solution I...
  17. G

    Lateral Area and Volume of a Pyramid

    Homework Statement A square pyramid has a slant height of 25 m and a lateral area of 350 m2. Which is closest to the volume of the pyramid? Homework Equations A = 2sb+b^2 V = SQRT(2)/6*b^3 The Attempt at a Solution 350 = 2 (25) b + 0 -> b = 7m (B^2 is 0 since it is lateral area only) V =...
  18. O

    Lateral edges of a pyramid

    Hi, I wonder if each lateral edge of a pyramid can be perpendicular to one of base's edge? The base is a tetragon. (If it is possible what a tetragon should it be and if it is not why) Can you help me, please? This is my first post so I want you to be understanding :shy:
  19. I

    Finding total outward flux through a pyramid?

    Homework Statement Let F=xi-yj+zk and the pyramid be as shown below. Find \iint\limits \,F\bullet dS as a surface integral over all five faces. The attempt at a solution I first solved it using the divergence theorem. The divergence was just 1, so the answer should just be the volume of...
  20. D

    Understanding Pascal's Pyramid & Internal Entries

    I have heard that Pascal's pyramid is a 3-dimensional analogue of Pascal's triangle . The edges of Pascal's pyramid come from a particular row in Pascal's triangle. For example, let's take the row of Pascal's triangle having entries 1 5 10 10 5 1. So, the corresponding Pascal's Pyramid...
  21. P

    How do I locate the centroid and the center of gravity of a square pyramid?

    Height=104 Base=220 x 220 Density=2500
  22. F

    What is the total electric flux through a pyramid with a point charge inside?

    Homework Statement a point charge of .04144 uC (micro C) is inside a pyramid. determine the total electric flux through the surface of the pyramid in units Nm^2/C Homework Equations The Attempt at a Solution i really don't know, i don't feel like there is enough information given.
  23. J

    Calculating Vertical Distance of a Thrown Pebble from a Pyramid

    Homework Statement A pebble is thrown off the side of a pyramide perpindicular to its slope. Find the vertical distance h under the assumption the drag forces are negligible. Homework Equations The Attempt at a Solution vx=vcos(90-Q) Q = theta vy=vsin(90-Q)...
  24. B

    Surface Integral of a Square Pyramid

    Homework Statement Prove that the following surface integral for the four slanted faces of a square pyramid with a square base in the xy plane with corners at (0,0) (0,2) (2,0) (2,2) and a top vertex at (1,1,2) is equal to 4 by evaluating it as it stands: \int\int (\nabla \times V)\cdot n dS...
  25. R

    Volume of a Pyramid: 474 ft & 11.0 Acres

    [b]1. A pyramid has a height of 474 ft and its base covers an area of 11.0 acres. The volume of a pyramid is given by the expression V = 1/3 Bh, where B is the area of the base and h is the height. Find the volume of this pyramid in cubic meters. (1 acre = 43 560 ft2). Homework Equations...
  26. Mentallic

    Calculating Pyramid Height from 3 Circles

    Given 3 circles each of radius r, stacked up into a triangular pyramid shape, find the height of the entire structure. This might be expressed more clearly in a graphical form: http://img206.imageshack.us/img206/3646/stackcircleseb0.png http://g.imageshack.us/img206/stackcircleseb0.png/1/...
  27. N

    Comp Sci Creating a Pyramid in C++: A Step-by-Step Guide

    I need to do a pyramid in C++ like this one: * * * * * * * * * * * * * * * buti just know how to do the figure at one side: * * * * * * * * * * * * * * * # include <stdio.h> # include <math.h> void main() { int count,count2...
  28. S

    Electric Flux through a Pyramid

    Homework Statement A pyramid with horizontal square base, 6.00 m on each side, and a hieght of 4.00 m is placed in a vertical electric field of 52.0 N/C. Calculate the total electric flux through the pyramid's four slanted surfaces. Homework Equations Phi = E*A*cos(theta) The...
  29. P

    Moment of Inertia of a Pyramid

    Homework Statement Ok not really a school problem but i was just thinking of how to solve it. How would i find the moment of inertia of a pyramid with base side length l and height h? If the axis of rotation is along the z axis? Homework Equations I = Summation of mrsquared The...
  30. P

    Square Pyramid Gauss's Law Trouble

    Homework Statement A pyramid with horizontal square base, 6.00 m on each side, and a height of 4.00 m is placed in a vertical electric field of 52.0 N/C. Calculate the total electric flux through the pyramid's slanted surfaces. Homework Equations Electric Flux = E dot dA The...
  31. B

    Help with pool ball pyramid problem

    Three identical spheres lie in contact with one another on a horizontal plane. A fourth sphere rests on them, touching all three. Show that, in equilibrium, the coefficient of friction between the spheres is at least (rad(3)-rad(2)) and that the coefficient between each sphere and the plane...
  32. L

    Calculating Volume of a Pyramid Frustum with Square Base and Top

    Find the volume of frustum of a pyramid with square base of side b, square top of side a, and height h. Usually when I do these volume problems, I treat them as an equation rotating around an axis, but this object has flat sides so I don't know how to begin...
  33. rohanprabhu

    Is this New Laptop Project a Scam?

    i know this is a physics forum.. but I'm more or less used to spam in the 'General Discussion' forum at most boards.. so.. somebody introduced me to this new 'project', where I could get a laptop for Rs. 10,000 [a kind of laptop which normally would cost me Rs. 35,000]. I was directed to this...
  34. P

    Is Silbury hill near stonehenge an egyptain pyramid?

    You often hear people talking about stonehenge but not so many people have heard of its close neighbour Silbury Hill - the biggest man-made hill in Europe.Silbury Hill was constructed at around 2700 BC about the same time as the Step Pyramid in Egypt. Is Silbury Hill a representation of a...
  35. P

    The mysterious underwater pyramid at Yonaguni in Japan

    This has intrigued me, mainly because a lot of the scientists that go and see it for themselves change their mind and end up thinking that it is not a natural formation. It is an absolutely huge stone monument off the coast of Japan, and it has right angle sides, parrallel ledges, steps, and...
  36. D

    How does the weight distribution work in a human pyramid?

    Hi! I'm Simone, I come from Italy and I'm a newbie..glad to meet you...and ehm...I have already a question! My question is related about the example of human pyramid. There are 5 people, one at top of the other..like: o1 o2 o3 o4 o5 o5 push o4 up...o4 push o3 up and so on.. the...
  37. M

    How Can You Prove <)APB+<)CPD=180' in a Base-Quadrilateral Pyramid?

    There is a base-quadrilateraled pyramid ABCDS , which base is quadrilateral ABCD. Inscribed sphere is tangent in point P on the ABCD wall. Proof that <)APB+<)CPD=180' I don't like geometry and i really don't know how to start.
  38. J

    Very interesting, a pyramid and sphere inscribed

    A pyramid ABCDS is given (the base is convex quadrilateral). A sphere is inscribed in this pyramid and it is tangent to side ABCD at point P. Prove that \angle APB + \angle CPD = 180^{o}
  39. H

    Solving the Pyramid Theorem: Explaining Eudoxus' Method

    My math teacher handed this out today without explaining, and told us to try and solve it. He gave us the formula to solve the volume of a pyramid (1/3 x area of base x height) and told us to explain WHY it was like that. I already figured out how to explain the surface area of the tetrahedron...
  40. P

    What is the height of the scaled-up Pyramid of Egypt?

    My Dad has a miniature Pyramid of Egypt. It is 3 inches in height. Dad was invited to display it at an exhibition. Dad felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1/ 9) times the density of the material used for the miniature. He...
  41. V

    Potential energy, a pyramid, and calculus

    I have a question involving calculus and Mechanics. It's from AP french, question 10-12. There's a pyramid with a square base of side, b, length 230m, and height, h, 150m. The density, p, of the pyramid is 2500kg/m^3. We are asked to find the total potential energy, PE of the pyramid taking the...
  42. J

    C/C++ How to Create a Pyramid in C++?

    Hello, I am trying to print an equilateral triangle, made up of * (stars), of height 8. Can someone please give me some hint. I am not getting the desired output. Thank you. Here is my code. #include<iostream.h> #include<iomanip.h> void main() { int n=8; for (int row=1...
  43. S

    How would I find the volume of a pyramid

    How would I find the volume of a pyramid with an equilateral triangle as it's base? I know how to do a pyramid with a square base (the integral from 0 to it's height of 2*(equation solved for y of a side)^2 dy)). Would this be the same method?
  44. P

    Calculating the Angle of a Pyramid and Square

    At my math exam i got this picture of a piamide. Now the question was to calculate the angle made by [tc] and the square (abcd) how much is that angle? my thougth was 37°45' and some "can you help me, with a calculation? the pictur is an attachement and also can be found @...
  45. S

    Great Pyramid of Cheops (Center of Mass Problem)

    The Great Pyramid of Cheops at El Gizeh, Egypt, had a height H = 148.6 m before its topmost stone fell. Its base is a square with edge length L = 227.4 m. Its volume V is equal (L^2)H/3. Assuming that it has uniform density p(rho) = 1.8e3 kg/m^3. (a) What is the original height of its center...
  46. F

    The base of the pyramid is 100 blocks by 100 blocks

    i need help with this problem The base of the pyramid is 100 blocks by 100 blocks; each successive layer is one less block wide and deep, until the top layer which is simply one block. Each block is 97 cm wide by 97 cm deep by 63 cm tall. If one liter of paint can coat exactly three square...
  47. N

    What secrets does the Great Pyramid of Giza hold?

    http://www.europa.com/~edge/pyramid.html I have a great deal of confidence in the ancient Egyptians, but not this much. I'm sure that some of these facts must be exaggerated, but I'm not much of a debunker. Some help would be appreciated.
  48. V

    What is the lateral area of a pyramid with given side length and heights?

    This problem is really getting to me, and I don't know why... INfo: Pyramid, Side length = 300 ft, perpendicular height = 321 ft, and slant height = (work shown later) 1. Find the slant height. Round your answer to the nearest whole number. (slant height)^2 = (height)^2 + (.5(side))^2 =...
  49. chronon

    Try to Arrange Squares 1-24 into 70 Side Square Pyramid Puzzle

    Following a post in the Number theory forum, I got to thinking: is it possible to arrange the squares with sides 1 to 24 into one big square of side 70. I think its probably impossible, but I've written an applet at http://www.chronon.org/applets/pyramid.html for people to try it out.
  50. S

    Work problem, deals with great pyramid

    this is a calc problem, but I thought it fits better here than in the math section since its homework. Here it goes: the great pyramid of cheops is 410 feet tall and 755 feet square at the base. find the volume of the pyramid using calculus. Part two: The stone used in constructing...
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