







Constructing a hexagonal pyramid 
20190425 

From REBECCA: I'm doing a project for my Honors Geometry class and I have to build a regular hexagonal pyramid. I was given the volume of .75 gallons, but I don't know how to figure everything else out. Please help?
Thanks,
Rebecca Answered by Harley Weston. 





A volume expression for a pyramid 
20180423 

From Shaheer: Do a three sided pyramid and a square pyramid have the same formula if you want to calculate the volume? Answered by Penny Nom. 





The volume of an attic 
20170907 

From paul: trying to determine volume of an attic base is rectangular 29 ft by 37 ft
peak runs parallel to longest base side and is 7 ft long
roof lines run from each end of the peak to the respective corners
the peak is 3.5 ft above the base
(so seen from above there are 5 visible lines: the peak and 1 line to each of the 4 corners) Answered by Harley. 





The surface area of a hexagonal pyramid 
20170616 

From Emilie: Hello, I need help with this question:
A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.
Thank you in advance if you can help me... Answered by Penny Nom. 





Building a pyramid 
20161201 

From Jesse: I'm trying to build a 30"by30"by 18.25"tall pyramid,what should my cutting measurements be? Answered by Harley Weston. 





The volume of a hexagonal pyramid 
20161021 

From Elizabeth: Find the height of a hexagonal pyramid with a volume of 1320 ft ^3. The area of the base is 120 ft^2. Answered by Penny Nom. 





Hexagonal pyramid bevel angles 
20160930 

From Peter: I have seen your response to a similar question from Steve which Chris and Harley responded to, however I am not familiar with some of the terms. Is there a formula that I can enter my details in which will give me the specific angles I require. The item I am constructing is much larger than the one you responded to previously. Thank you for any assistance you are able to provide. Answered by Penny Nom. 





The volume of a truncated rectangular pyramidal pond 
20160513 

From Paul: How do you calculate a partially filled truncated rectangular pyramid if you always know the bottom rectangle, the maximum height top rectangle perimeter, but have a varying height. Similar to filling up a pond you know the current height and dimensions at the max rectangle how do you calculate it half full i.e. 10x30 outside perimeter with a 2x8 base and a max height of 6ft how do you calculate it at 3ft without remeasuring the top perimeter.
Thanks,
Paul Answered by Harley Weston. 





Sierpinski Pyramid 
20151214 

From victor: Is a tetrix (a Sirpienski Pyramid/Tetrahedron) its own hyperplane?...alternatively, is it a hyperplane? Answered by Robert Dawson. 





A truncated, squarebased pyramid 
20141123 

From Hannah: A designer vase has the shape of a truncated, squarebased pyramid. The base of the vase is a square with a side length of 15 cm. The area of the square opening is 70.56 cm2. Each of the four sides is a trapezium with slant sides 9 cm long. Find (to the nearest square centimetre) the total surface
area of the vase. Answered by Penny Nom. 





A truncated squarebased pyramid 
20141022 

From Beth: How do you find the height of the original squarebased pyramid when given the sides (12cm) of the base and height (6cm) of the truncated pyramid, as well as the sides (3cm) of the base of the chopped off top (chopped off parallel to the base)? Answered by Penny Nom. 





A small solid silver pyramid 
20140613 

From Jenesis: For Awards Night at Baddeck High School, the math club is designing small solid silver pyramids.The base of the pyramids will be a 2 in by 2 in square. The pyramids should not weigh more than 2.5 pounds. One cubic foot of silver weighs 655 pounds. What is the maximum height of the pyramids? Answered by Penny Nom. 





The volume of hexagonal pyramid and hexagonal prism 
20140518 

From visshwam: how to find volume of hexagonal pyramid and hexagonal prism?
my measurements are each side of pyramid's triangle is 1"x2"x2".
hexagon prism is 2"x1" each side Answered by Penny Nom. 





A frustum of a pyramid with a square base 
20140418 

From tuba: a pyramid has a base of 10 m and is 15 m high.what is the volume? if 6m is removed from top what is the volume of the remaining frustum? Answered by Penny Nom. 





The volume of a pond 
20130814 

From Kelly: I have a pond that measures 335 feet wide, 385 feet long and 18 feet deep with a 4:1 slope on all four side. How do I figure out how many gallons of water this pond will hold? Answered by Harley Weston. 





The surface area of a pyramid 
20130611 

From Sam: A right rectangular pyramid has a rectangular base measuring 18 cm by 32 cm. The height of the pyramid is 12 cm. What is the surface area? Answered by Penny Nom. 





A gravel pile in the shape of a triangular pyramid 
20130404 

From Casey: Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.
I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.
Thank you for any help.
Casey Answered by Penny Nom. 





Question 
20130404 

From Casey: Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.
I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.
Thank you for any help.
Casey Answered by Penny Nom. 





Cones, pyramids, cylinders and prisms 
20120913 

From Roy: I read on this page that a pyramid is a special kind of cone, but a cone is not a pyramid. Does this apply to cylinders. Is a prism a special kind of cylinder, but a cylinder is not a prism? Answered by Robert Dawson. 





A pyramid on a regular hexagon 
20120414 

From deepak: There is pyramid on a base which is a regular hexagon of side 2a cm.
If every slant edge of this pyramid
is of length 5a/2 cm, than what will be the volume of this pyramid Answered by Penny Nom. 





A pyramid and Pythagoras 
20111015 

From ele: On square based pyramid, the lengths of the sides of the base are all 2m. The height from the top of the pyramid to the middle of the base is 0.5m. What are the lengths of the sides of the triangular pieces and the contained angle? Answered by Penny Nom. 





Building a custom range hood 
20111008 

From Bill: I'm building a custom range hood for a customer with special order material that matches
their newly installed cabinets and I need it to be perfect. The hood is basically a pyramid
but the 4th side is the flat wall at the back and a flat, rectangular top. I need to calculate
the bevel and miter of the three sides but I never was very good with geometry functions
(although I am fairly good with other math fields). I either need the calculations from you
at least (shudder) a formula or set of formulas so that I can calculate them myself. Answered by Harley Weston. 





The volume of a triangular pyramid 
20110415 

From Chelsea: There is a triangular pyramid which is an equilateral on the base with all sides 16.5 and the height is 25. I have to find the volume. Please help! Answered by Penny Nom. 





The volume of a hopper 
20110413 

From michael: I have a tank that is 72" x 72" at the top and 10" x 10" at the bottom
and is 31" tall. I need to calculate the cubic feet of the tank Answered by Penny Nom. 





Slicing a rectangular parallelepiped 
20110223 

From tom: a) Pass a plane containing a vertex of a rectangular parallelepiped and a
diagonal of a face not containing that vertex to cut a pyramid from the
parallelepiped. What fraction of the volume of the parallelepiped is the
volume of the pyramid thus cut off?
b)Pass a plane through a cube of edge 8 in so that the section formed
will be a regular hexagon. Through each side of the hexagon pass two
planes, one plane containing one of the two vertices of the cube
which are farthest away from the plane of the hexagon, the other
plane containing the diagonally opposite vertex of the cube. Find the
volume of the solid bounded by these planes.
c)three of the edges of a rectangular parallelepiped that meet in a point
are also the lateral edges of a pyramid. What fraction of the parallelepiped
is this pyramid...?
you know the my only problem is how to illustrate this one...if only i
could ...can you help me....all I need is the drawing and I can do the rest
..it's fine if you'll only answer any of these but I'll be thankful if you
will do the three :).... Answered by Penny Nom. 





The volume of a truncated pyramid 
20101012 

From A: what is the formula to find out volume of a pyramid with individual length and breadth? For example bottom size is 6.5m x 6.5m, top size 1.5m x 4.2m and height 0.8m. please send me the formula. Answered by Stephen La Rocque. 





A square pyramid 
20100526 

From Georgia:
Question from Georgia, a student:
I have been given the following question in a maths assingment, and have so far been unable to answer it.
To begin, i am required to draw a square pyramid as follows:
1. draw a 3 dimensional diagram of a square based pyramid
2. label the square base as ABCD, call the vertex H.
3. Mark in E and F the midpoints of AD and BC respectively and O is the midpoint of EF
Note: this therefore makes FO = FC
this i was fine with, it was the following question that stumped me.
1. if the height of the pyramid is 280m, what is the length of the base?
Thanks, Georgia Answered by Chris Fisher. 





A champagne tower 
20100416 

From gabriel: thanks for having something like this up online. My question is how do i build a Champagne Tower that has 290 glasses and 15 stories high.
Please help me out. this is for a clarity function. Answered by Robert Dawson. 





Pyramids and parallelograms 
20100401 

From Vivi: Hi, my name is Vivi, and math teacher is giving a geometry test. I tend to forget how to find the surface area and volume of triangular pyramids and parallelograms. Do you have a way of remembering how to find the surface area? Answered by Harley Weston. 





A champagne pyramid 
20100322 

From Kathy: I have 680 champagne glasses and my pyramid can only be 15 levels high. How many glasses need to be on each level? Is there a formula I can use? Answered by Robert Dawson. 





The volume of a frusta of a hexagonal based pyramid 
20100304 

From sarah: Volume of a frusta of a hexagonal based pyramid Answered by Penny Nom. 





A prism and a pyramid 
20100219 

From Juanita: What is the relationship between the volume of a prism and a pyramid with congruent base areas and heights? Answered by Tyler Wood. 





A triangular pyramid 
20100105 

From ally: how many vertices, edges, faces in a triangular pyramid? Answered by Robert Dawson. 





The surface area of a rectangular pyramid 
20090713 

From Shivani: What is the surface area of a rectangular pyramid with a length of 6 inches,
a width of 7 inches and a SLANT height of 4 inches. Answered by Penny Nom. 





A six sided pyramid 
20090511 

From Karen: I am going to make my kids a six sided tipi (pyramid) I have a 5 foot tall central pole, and I would like the floor area to be 6 feet across. How do I work out what size to cut each fabric panel to make this happen? Answered by Harley Weston. 





A toy pyramid 
20090403 

From Darah: Suppose you want to build a toy pyramid with a square base and a volume of 9000 cubic centimeters. What are the dimensions of a pyramid you might design? How many such pyramid designs are there? Answered by Stephen La Rocque. 





Square prisms and pyramids 
20090403 

From Sheyna: What are the differences between a square prism and a pyramid?
 Sheyna Answered by Penny Nom. 





A polyhedron 
20090310 

From Mollie: Hi, my name is Mollie and I'm in 5th grade. Here's the math problem I have for homework tonight:
"Larissa made a model of a polyhedron using 8 pieces of clay for the vertices and 18 straws for the edges. What type of
polyhedron did Larissa make?"
Thanks. Answered by Penny Nom. 





Symmetries of a polyhedron 
20090302 

From Vincent: I want to ask is there a formula to find out the number of axes of rotation & plane
of reflection of a 3D figure, like pentagon, pyramid? Answered by Chris Fisher. 





A triangular pyramid 
20090226 

From Craig: Can you help with this question:
Write the names of the faces and the number of each kind of face on a triangular
pyramid? Answered by Penny Nom. 





An octagonal pyramid 
20090220 

From JUDY: THE BASE OF A PYRAMID IS A REGULAR OCTAGON. HOW MANY CONGRUENT TRIANGULAR FACES DOES THE PYRAMID HAVE? Answered by Penny Nom. 





Solid figures 
20090210 

From Rebecca: I need to know the names of solid figures. I have several pictures that I need to answer what type they are.
Thanks, Rebecca 3rd grade Answered by Penny Nom. 





A triangular pyramid 
20090206 

From kamran: what would be an example of a triangular pyramid Answered by Stephen La Rocque. 





Faces, edges and vertices 
20090204 

From sheila: what is the relationship between the number of faces and the number of edges of a triangular pyramid ? Answered by Penny Nom. 





A flattopped pyramid 
20090110 

From Tom: I am planning to build an open ended, flattopped pyramid with a
rectangular base 28 x 36 in.; a square top 6 x6 in.; and a vertical
height of 16 in.
I know how to calculate the dimensions of each of the pyramid sides but
I don't know how to calculate the interior angles when I bend the sheet
metal. I will cut the four sides separately and add a one inch flange
to each "vertical" edge of the two larger sides to allow for
a bonding surface for the assembly. How do I calculate that angle? I
know it will be greater than 90 degrees but by how much? Answered by Harley Weston. 





Triangular prisms and pyramids 
20090110 

From KJ: What are some items found in a home or school that could be considered a triangular prism or triangular pyramid? Answered by Robert Dawson and Penny Nom. 





The base of a triangular pyramid 
20081220 

From joe: triangular pyramid
base height=
base width=8ft
height=6ft
volume=88ftcu.
Please explain base height & how to solve. Answered by Penny Nom. 





The volume of a feed hopper 
20081218 

From John: I need to calculate the volume of a feed hopper, and I'm not sure how to break it down. The top of the hopper is 36" x 36", it is 30" deep, and ends at a 6" x 6" plate. One side of the hopper is straight top to bottom, of course tapering on two sides to meet at the plate. The other three sides angle down at about 75 degrees. I need to determine the cubic foot volume of this hopper (it is used for ground coffee) so I can configure a vibrator to knock down residual grounds. Thanks. Answered by Robert Dawson. 





An irregular, truncated pyramid 
20081024 

From phillip: Hi, I have a rectangular base to square top, pyramid shape to fabricate out
of steel plate (4 sections). The base is 3000mm by 800mm, the height is
1100mm and the top is 350mm square. What I need to know is the
lengths of the sides of the plate(were they meet vertically). Hope ive made
it clear enough. Thanks Phil. Answered by Stephen La Rocque. 





Nets of SquareBased Pyramids 
20081010 

From Miss: How many different nets does a squarebased pyramid have? Answered by Janice Cotcher. 





The angle between two faces of a pyramid 
20080806 

From Carla: A pyramid has its vertex directly above the centre of its square base.
The edges of the base are each 6cm, and the vertical height is 8cm.
Find the angle between 2 adjacent slant faces. Answered by Penny Nom. 





Some angles in a pyramid 
20080804 

From Carla: A symmetrical pyramid stands on a square base of side 8cm. The slant height of
the pyramidis 20cm. Find the angle between the slant edge and the base, and the angle between
a slant face and the base. Answered by Penny Nom. 





Finding Angles in a Pyramid 
20080730 

From Carla: A pyramid has its vertex directly above the centre of its square base. The edges of the base
are each 8cm, and the vertical height is 10cm. Find the angle between the slant face and the base,
and the angle between the slant edge and the base. Answered by Janice Cotcher. 





The volume of a hexagonal pyramid 
20080605 

From Angie: My son is working on a hexagonal pyramid. The base is 4 and the slant height is 6. We know that the answer is 48 times the sqrt of 2. We don't know how they got it. We attached the drawing of it. Answered by Penny Nom. 





The area of a regular hexagonal pyramid 
20080510 

From Kim: i need help finding the area of a regular hexagonal pyramid. Answered by Penny Nom. 





What shape(3D) has 5 vertices,8 edges,and 5 faces? 
20080425 

From stacy: what shape(3D) has 5 vertices,8 edges,and 5 faces? Answered by Penny Nom. 





A chain letter 
20080410 

From Lesley: In the mail you receive a chain letter with a list of ten names on it. The instructions tell you to send $2 to the person named on the top of the list, cross his name out, and place your name on the bottom. YOu then have to send ten copies of this letter to friends with the same instructions. If no one breaks the chain how much money should you receive? Answered by Stephen La Rocque and Harley Weston. 





The number of faces and vertices in a pyramid 
20080402 

From Laurie: Can you find a connection between the number of faces and vertices in a pyramid and the number of sides of it's base??? Answered by Penny Nom. 





Triangular prisms and pyramids 
20080303 

From LORENA: hi i am in yr 6 and i need to know how many faces,vertices and edges these shapes have..
. TRIANGULAR PYRAMID
. TRIANGULAR PRISM Answered by Penny Nom. 





A step pyramid 
20080219 

From Patty: On a step pyramid  do you count each side of the step as a face?
 and each corner a vertex?  How do I find the volume of a step pyramid? Answered by Stephen La Rocque. 





The volume of a pyramid 
20080203 

From Britni: The base of this pyramid is an equilateral triangle with sides 8 units.
The altitude of the pyramid is square root of 3. What is its volume? Answered by Penny Nom. 





Cones and pyramids 
20071110 

From Eric: I have a question regrading the differences between a cone and a pyramid.
In my son's Maths workbook, a cone is always referred to as a pyramid,
which confuses me very much. I understand that a pyramid is a special case of a
cone and therefore you can refer a pyramid as a cone but not the other way around.
Am I correct? Answered by Harley Weston. 





The volume of a pyramid 
20071031 

From San: the volume V of a squarebased pyramid with base sides s and height h is V=1/3s2h if the height is half of the length of a base side, express the volume V as a function of s Answered by Penny Nom. 





Water flowing into a tank 
20070921 

From andrew: Hi, I've been having real trouble visualizing this problem as apposed to a conical tank.
It says the base of a pyramidshaped tank is a square with sides of length 12 feet. The
vertex of the pyramid is 10 feet above the base. The tank is filled to a depth of 4 feet, water is flowing
into the tank at the rate of 2 cubic feet per minute. Find the rate of change of the depth of water in the tank. Answered by Harley Weston. 





A frustum of a right pyramid 
20070824 

From Andrew: Find the volume of a frustum of a right pyramid whose lower base is a square with a side 5 in., whose upper base is a square with a side 3in., and whose altitude is 12 in. Round your answer to the nearest whole number.
A. 47cu in. C. 226 cu in.
B. 196 cu in. D. 1036 cu in. Answered by Stephen la Rocque. 





The volume of a hexagonal pyramid 
20070805 

From monica: what is the volume of a hexagon when the base of one triangle is 6cm and has the height of 5.1cm the height of the regular hexagonal pyramid is 18cm? Answered by Penny Nom. 





Prisms and pyramids 
20070802 

From taryn: two similarities between prism and pyramid Answered by Penny Nom. 





A triangular pyramid 
20070722 

From shani: my homework question is confusing (yr 7 beginner)
"How many vertices does a triangular pyramid have."
(Mum thinks all triangles are triangular& vertices are sides)
I want to be sure. Answered by Penny Nom. 





The area of a triangular pyramid 
20070718 

From Jhezelle: What is the formula of finding the surface area of a triangular pyramid? Answered by Penny Nom. 





The number of blocks on the face of a pyramid 
20070627 

From Heather: I was wondering if there was an equation in order to calculate the number of blocks on the face of a pyramid.
For example:
X
X X
X X X
Is there a specific formula in order to calculate that there are
6 blocks here?
Thank You,
Heather Answered by Harley Weston. 





Hexagonal pyramids 
20070517 

From Tracey: How many faces, edges, and vertices does a hexagonal pyramid have? Answered by Stephen La Rocque. 





Area and a squarebased pyramid 
20070508 

From Nick: For a regular square pyramid with base perimeter 40 and slant height 50, what is the lateral and surface areas? Answered by Stephen La Rocque. 





A pyramid with 15 faces 
20070505 

From Nick: A pyramid has 15 faces. What shape is its base and how many edges does it have? Answered by Penny Nom. 





The area of a pyramid 
20070428 

From Alexander: Total area of the plate required to fabricate a vessel(pyramid) the base is 0.6mx0.6m and height of 1.0m. Answered by Stephen La Rocque. 





The vertices of a hexagonal pyramid 
20070426 

From Madeline: How many vertices does a hexagonal pyramid have?? Answered by Penny Nom. 





A pentagonal pyramid 
20070410 

From Alan: Help me please, I'm pretty stumped here. I guess I'll start with the measurements I do have.
The pentagon base of the pyramid is inscribed in an eight inch circle, giving each side the
measurement of 4 & 5/8 inches.
I have two glass billets measuring 5"x10"x3/4"
If I did the math right I need the form to hold about 75 cubic inches.
What does the height of the pyramid need to be to hold the volume of the two billets? (note: the billets
will be broken into smaller pieces to actually fit into the form.) Answered by Stephen La Rocque. 





Names of solid figures 
20070328 

From Debbie: What is the name of the solid figure: 1) base with 5 equal sides and faces that are 5 triangles 2) all 6 faces are squares and 3) 2 congruent pentagons for bases and 5 rectangular faces. Please help! Thanks Answered by Penny Nom. 





A hexagonal prism 
20070320 

From makiya: i need help trying to find the surface area and the volume of a hexigon that has an edgde length of 6cm and a hieght of 12 cm
i allready know how do do this by breaking it into triangles and finging the surface area and the volume that way i just need to know how to find a faster formuly that aplies to just hexigons thanks makiya Answered by Penny Nom. 





The height of a hexagonal pyramid 
20070307 

From Carol: i have been set a question that gives a regular hexagon and each of the sloping sides is 6cm from a corner of a base to the apex(point). it also has 2cm sides it looks sort of like this: /\6cm 2cm Answered by Penny Nom. 





The net for a pentagonal pyramid 
20070305 

From MaKayla: How many bases does the net for a pentagonal pyramid have? Answered by Penny Nom. 





The altitude of regular nside pyramid 
20070126 

From Wendimu: The altitude of regular nside pyramid is half of it's base side.What is the angle between the lateral face and it's base? Answered by Penny Nom. 





A regular pentagonal pyramid 
20070125 

From Vickifazio: a regular pentagonal pyramid has a base perimeter of 1,085 ft. How long is one side of the base? Answered by Stephen La Rocque. 





The volume of a frustum of a pyramid 
20070117 

From Sam: Find the volume of a frustum of a pyramid with square base of side b, square top of side a, and height h. Answered by Penny Nom. 





A pyramid project 
20061118 

From Becka: i'm doing a pyramid project and i'm having some trouble with the dimensions. if my base is 14in. then what should my angle and height be? Answered by Penny Nom. 





Pyramids and cones 
20060606 

From Melissa: I was wondering if a cone can be considered a pyramid. Looking at many definitions of pyramids I have read that pyramids come to a common vertex. A cone comes to a vertex. But I also read that pyramids all have triangular faces. In this case a cone would not be considered a pyramid. Am I correct? Answered by Chris Fisher. 





What defines a pyramid? 
20060425 

From Julie and son: My son and I think that a pyramid can have any number of sides, but my son's teacher says a pyramid has just 4 sides (including the base). Who's right? Answered by Stephen La Rocque. 





The volume & surface area of a rectangular pyramid. 
20060227 

From Cheryl: My daughter is working on a math project & we are having a hard time finding the volume & surface area of a rectangular pyramid. Can you help us with this? Answered by Penny Nom. 





Why 1/3 in the volume formula for a pyramid? 
20060203 

From Becky: why is the formula for finding the volume of a pyramid divide by 3? Answered by Penny Nom. 





A block pyramid 
20051105 

From Kyle: if i make a block pyramid and it puts a new perimeter around it every time, for example the first layer will be 1 block across (area=1), the second layer will be 3 blocks across (area=9), the third layer will be 5 blocks across (area=15),etc. The normal block pyramid. I have figured out that in order to figure out the number of blocks needed for a certain level, the equation is (2x1)2 or (2x1)(2x1), where x is equal to the level. For example, on the fourth level, the equation tells you that it will have an area of 49. How would i make an equation for the total number of blocks up to the level. For example, in order to complete 1 level you need 1 block, for 2 levels you need 10 blocks, for three levels you need 35 blocks, and for 4 levels you need 84 blocks. Answered by Penny Nom. 





A triangular pyramid 
20051022 

From Stacee: When stacking oranges to form a triangular pyramid, each orange touching 3 oranges below it. In order to have a pyramid with 6 layers, how many oranges should be on the bottom layer? Answered by Penny Nom. 





Painting a pyramid 
20050913 

From Cindi: 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 meters how many liters are required to coat the entire exposed surface of the pyramid? Round up to the nearest liter. Answered by Penny Nom. 





Surface areas 
20050511 

From Jessica: How can I demonstrate to my high school students the reason for the formulas for the surface area of a prism, right cylinder, and regular pyramid, and right cone? Answered by Penny Nom. 





A pyramid 
20050424 

From Marc: I'm helping my daughter build a pyramid,it needs to be 30cm in height. I have cut out four pieces at 30 deg angles. When I went to join up the pieces it did not fit. I recheck my measuments and found that they were correct. Do I need to cut two pieces smaller so they can match up? Did I cut them at the wrong angles. My base is also 30cm, is that my problem? Answered by Chris Fisher and Harley Weston. 





A 6 sided (hexagonal) pyramid 
20050122 

From Steve: im trying to make a 6 sided (hexagon) pyramid, from 6 triangles of 12mm plywood, i know all the angles to cut apart from the one one to join all 6 triangles together. Rough measurements are outer edge (A) of each triangle is 13cm's, length of other 2 sides (B&C) of triangle outside to center is 14cm's with a height of the whole thing together about 6cm's. Answered by Chris Fisher and Harley Weston. 





Making a pyramid 
20040912 

From Jacob: My name is Jacob and I am a 11th grade student trying to build a pyramid for a friend but I need a chart of some sort to show me the measurements (I learn better w\pictures) it is a square base with 18 in sides and I want the vertex to be 18in above the base I need to know as many measurements as you can give me. Answered by Penny Nom. 





The surface area of a pyramid 
20040619 

From Jason: I was wondering how to find the area of a pyramid when you donít know the height of the face but the height of the Pyramids highest point? Answered by Penny Nom. 





A pyramid 
20040511 

From Quiana: I am a student and I have the following questions I need to answer for homework:
How many sides, vertices, and edges does a pyramid have? Answered by Penny Nom. 





A pyramidshaped tank 
20040213 

From Annette: The base of a pyramidshaped tank is a square with sides of length 9 feet, and the vertex of the pyramid is 12 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at a rate of 3 cubic feet per second. Find the rate of change of the depth of water in the tank. (Hint: the volume of a pyramid is V = 1/3 B h , where B is the base area and h is the height of the pyramid.) Answered by Harley Weston. 





A pyramid with its top cut off 
20030721 

From David: What is the name given to a 3D shape that looks like a pyramid with its top cut off? Answered by Penny Nom. 





Nets for pyramids 
20020214 

From Michelle: I want to have my students create nets for pyramids and I need to know how to find the correct range of degrees for the interior congruent angles of the isosceles triangular faces. For example, I know for a squarebased pyramid that 77 degrees will work; however, I know other angle measures will also work. I'm just not sure how to find the minimum degree measure to have the net actually "work". I'm assuming the maximum would be 89 degrees, although that would make for a very tall pyramid. Answered by Penny Nom. 





The slopes of the sides of the Great Pyramid 
20020209 

From Christina: The Great Pyramid is the largest of the Egyptian pryamids. When it was built, it was 481 feet tall and had a square base with 755foot sides. The pyramid has two different slopesone along its sides and the other along its edges. Which slope is steeper? Answered by Penny Nom. 





A triangular pyramid 
20010514 

From Kumar: In a Pyramid OABC, all the three sides of the base: a, b, c are known. Also known are the angles between the three sides from the vertex O: Angles AOB, BOC, COA. With this information, is it possible to calculate the lengths of the three sides: OA, OB & OC. Answered by Chris Fisher. 





The height of a pyramid 
20010511 

From Ryan: Jane is building a model of a pyramid for a history project. It has a square base of side length 100 cm. The angle of elevation of the sides is 60 degrees. What is the height of Jane's pyramid. Answered by Harley Weston. 





Pyramids 
20010418 

From Kelly: I'm in tenth grade and I know that there's some formula for finding out the slope of the side of a pyramid. I thought it could be the pythagorean therom, but I'm not sure if this works. Please send me the formula as soon as possible, I need it for a project. Answered by Penny Nom. 





Four questions 
20000317 

From Ibrahim Bin kasmin:
 What is a hexahedron?(please show a picture of a hexahedron).
 How do we make a cube out of three pyramids?(show me the picture).
 How do we find the approximate perimeter and area of a hibiscus leaf?
 What is a Pascal triangle?
Answered by Penny Nom. 





Building a pyramid 
20000226 

From Francis X. Hines Jr.: I am presently trying to build a pyramid. I can understand that the base has 90 degree angles on the first plane which is the outline of the square that makes up the floor. As close as I can figure the slope of each wall face is 35 degrees or 35.7 to be exact if I am correct by using 360 as the total of the three interior angles.Now , I run into a compound angle where the corners meet what would be the angle created by the two 35 degree angles that would allow for the 90 degree edge to continue. Because I'm working in three dimensions I also need to be sure that my math would be correct when I substract 35 from 90 to aquire the angle of the narrow edge as to allow for a 90 degree surface to be present ..to allow for another level to be added with only the base line being shortened. I hope you can understand what it is that I'm asking assistance with.I would greatly appericate your help. Answered by Chris Fisher. 





Pyramids and prisms 
20000118 

From Tyler: What's the definition of a Triangular Prism and a Triangular pyramid. Answered by Penny Nom. 





A Frustum 
19990329 

From Monica Armour: What do you call a square pyramid that has had the top chopped off? Answered by Chris Fisher and Jack LeSage. 





Cannonballs 
19990127 

From Roger King: How many cannonballs can be stacked in a triangular pyramid? Answered by Penny Nom. 





Pyramid 
19980504 

From Lisa Nathan: How do you find the area of a pyramid? Answered by Harley Weston. 





What is the volume of a regular tetrahedron? 
19961021 

From Paul Bleier: How does one calculate the volume and the height of a three sided pyramid formed by equilateral triangles? Answered by Bruce Gilligan. 





Solides d’Archimède 
20140429 

From Clémentine: Pourquoi une pyramide a base carrée n'est elle pas un polyèdre archimedien ?
J'ai pourtant essayé d'en construire un avec tout ses cotés égaux et ça fonctionne !
Aidez moi je n'en dors plus la nuit ? :S Answered by Chris Fisher. 

