2006-10-02 07:41:27 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
A lot of students wonder about this. The easiest way to prove it to a 14 year old would be to use Euclid's method of proving it.
Book XII, Proposition 7, Euclid's Elements - David Joyce
http://aleph0.clarku.edu/~djoyce/java/elements/bookXII/propXII7.html
This shows a way to divide a triangular prism into three pyramids of equal volume. The formula for a triangular prism is base x height. So it therefore follows that the formula for a triangular pyramid is 1/3 x base x height.
However, a little more work is needed to complete the proof for all pyramids, which Euclid does next. There's a link in that article to the follow on proof.
The complete (thorough) proof requires infinite series and would beyond the ability of most students at the level where the formula is taught (e.g. 14 yr. olds). However, if you have an astute teenager, point them to this explanation in the Dr. Math archives at:
http://mathforum.org/dr.math/problems/swan3.30.98.html
2006-10-02 07:47:05 · answer #1 · answered by Puzzling 7 · 2⤊ 0⤋
Think of a rectangular prism with the same base and height.
Now consider a pyramid with the same base and height.
Because of the difference in shape, notice how the pyramid would take up a portion of the rectangular prism, with room to spare. (Imagine slipping a rectangular prism over a pyramid, both having the same base and height).
The rectangular prism is larger, or in other words, the pyramid is smaller, and in this case, by a factor of a third.
2006-10-02 14:49:55 · answer #2 · answered by Link 5 · 0⤊ 0⤋
use a clay model of a cube of same base then cut out your pyramid and from the remaining clay make two more pyramids of same form
so volume =1/3 volume of cube = 1/3 area of base * height
2006-10-03 03:21:30 · answer #3 · answered by chaits89 2 · 0⤊ 0⤋
Sure. If you make a cube out of the base dimensions, show that you can make two pyramids out of the "rest of" the cube after taking out the pyramid. It'd be easy to show with a model.
2006-10-02 14:50:09 · answer #4 · answered by loon_mallet_wielder 5 · 0⤊ 0⤋
make a pyramid with base in 'X' shape and ht also in same 'X' shape; it will be a good task, but for u 'll be easy u r a teacher. Now cut the stucture from top into equal halves. cut also in horizontaly. U 'll get 4pcs thro one to make it three.
2006-10-03 01:26:15 · answer #5 · answered by positives 1 · 0⤊ 0⤋
Me thinks that you are the 14 year old who needs homework help. Nice try my friend.
2006-10-02 14:44:39 · answer #6 · answered by Ex Head 6 · 0⤊ 2⤋
who cares
2006-10-02 14:51:25 · answer #7 · answered by Venkat 2 · 0⤊ 2⤋