Pyramid volume
How many man hours did it take to build the great pyramid of Giza? Historians believe that the pyramid took about 20 years to build. With this number we can use a little math and physics to estimate the minimum number of people involved in the construction.
The first piece of information we need to know is how much volume the great pyramid has. When it was built, the pyramid had a height of about 150 m and the length of the square base was 230 m. What then is the total volume of the pyramid in m 3 ?
Image credit: Wikipedia Janusz Reclaw
The answer is 2645000.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
8 solutions
I didnt knew there was a formula for it but We could derive the formula easily with calculus.....
Pyramide is the 1/6th part of the cube....so here... L & B of cube is 230m & H is 300 m...so...
(230 230 300)/6=2645000
If you take six of these pyramids and put them together you do not have a cube.
Log in to reply
i dont think so just take six symmetric pyramid u can get a cube ( here height is half of the length of side of the base )
Log in to reply
I am talking about "these" pyramids, not pyramids that meet the requirements of a special case. "These" had a height of about 150 m and the length of the square base was 230 m.
Cuboid not cube...but good approach.
we can take it to be two tetrahedrons and also solve....as we can calculate the volume of one tetrahedron as A vector CROSS B vector DOT C vector whole time 1/6
dear plz explain what U did with Hight???? How is it 300m???? Although given is 150m only...... ????????
it is just like cone inside cylinder in that case base is circular but in this case base is rectangular.. so volume of cone is 1/3 area of circle height
here volume of pyramid=1/3 area of rectangle height =1/3 *(230)(230)(150)=2645000
The Volume of a pyramid with a rectangular base is given by V = 3 l × b × h where l = length of the base , b = breadth of the base ' and h = height of the pyramid.
Since in the problem it is given that we have a square base pf length 230 m and the height is 150 ,
The volume can be given by V = 3 2 3 0 × 2 3 0 × 1 5 0 (Being a square base length and breadth of the base are same ) .
which comes out to be 2 6 4 5 0 0 which is the correct answer.
V=( l w h)/3
V= (230m* 230m* 150m)/3
V= 2,645,000 m^3
150 x 230² / 3 = 2645000
Formula for Pyramid Volume is (Length * Height * Width)/3 So putting values (230 * 150 * 230)/3 = 2645000
The volume of any pyramid is equal to:-1/3 (area of square base)^2 (height of pyramid)
Can't anybody here derive the formula?
Log in to reply
Sure thing! The usual calculus approach is to just sum up a bunch of prisms - I wrote this formally but you can really do it without knowing any calculus and just using limits.
Let the dimensions of the enclosing prism for the pyramid be x , y , z with z as the height. Starting from the apex, descend a units along the z axis. Then the area of the plane at that point would be z 2 a 2 ( x y ) . Now that we're done with that, just integrate! ∫ 0 z z 2 a 2 x y d a = 3 z 2 z 3 x y − 0 = 3 x y z
The non-calculus approach (which was vaguely mentioned ) involves placing 6 pyramids in a way to create the enclosing prism stacked on itself.
First let us assume that the base is a square since given only one measurement Volume of a pyramid is given by V = 1 / 3 ∗ b ∗ h V = 1 / 3 ∗ ( 2 3 0 2 ) ∗ ( 1 5 0 ) v = 1 / 3 ∗ ( 5 2 9 0 0 ) ∗ ( 1 5 0 ) Doing elementary operations we get 2 6 4 5 0 0 0 as the answer.