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#1 2014-02-19 21:02:08
- thedarktiger
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- Registered: 2014-01-10
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stuff in a box
Let ABCDEFGH be a rectangular prism, as shown, where AB = 2, AD = 3, and AE = 5. Find the volume of pyramid ACFH.
Wow I how I'm a full member soon, so I can post pictures. So annoying ><
how to do this one? whats the volume of the parts surronding the pyramid? Is there a formula?
thanks!:P
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#2 2014-02-19 21:07:24
- Bob
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Re: stuff in a box
I'll make a diagram now.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2014-02-19 21:15:20
- Bob
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Re: stuff in a box
Is this it?
The cut away bits are all pyramids with similar properties. (There are 4 of them.) They all may be considered as having a right angled triangular base, and a vertical height of 5.
The volume of a pyramid is
so you can calculate them and subtract from the volume of the pyramid.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#4 2014-02-20 21:36:55
- thedarktiger
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Re: stuff in a box
Yes thats it! thanks.
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#5 2014-10-25 12:28:50
- SolarDevil
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Re: stuff in a box
What is the perpendicular height in this case?
Don't expect a reply for another 24 hrs... Thanks in advance
Solar Devil
Herro! Sycamore School will win National Science Bowl this year!!! 
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#6 2014-10-25 20:34:41
- Bob
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Re: stuff in a box
They all may be considered as having a right angled triangular base, and a vertical height of 5.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#7 2014-10-26 05:51:39
- SolarDevil
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Re: stuff in a box
Would the answer be 25\sqrt{29} all over 6?
Herro! Sycamore School will win National Science Bowl this year!!!
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#8 2014-10-26 20:35:52
- Bob
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Re: stuff in a box
hi SolarDevil
That's not what I'm getting. Please post all your working, so I can compare with mine.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#9 2014-10-28 11:48:12
- SolarDevil
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Re: stuff in a box
V=1/3*base area*height
V=5/3*base area
so
Area of base= rt29*3/2
So V=5rt29/6
oops 5rt29/6
Solar
Herro! Sycamore School will win National Science Bowl this year!!!
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#10 2014-10-28 20:47:41
- Bob
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Re: stuff in a box
The height has to be 'perpendicular to the base'. For this polyhedron, I'm unclear how you are calculating this. Look at post 3. My method avoids this difficulty by getting the volume of four 'easy' pyramids and subtracting from the volume of the cuboid. If I've got that right then the answer is an integer.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#11 2014-10-29 09:30:25
- SolarDevil
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Re: stuff in a box
Oh, I see. Thanks!
Herro! Sycamore School will win National Science Bowl this year!!!
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#12 2014-10-29 09:49:57
- droid347
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Re: stuff in a box
Nice problem! *cough* @SolarDevil *cough*
Aiming for USAJMO in 2015
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#13 2014-10-29 10:45:30
- SolarDevil
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Re: stuff in a box
Hi droid347! Welcome to the forum! and... yes it is a good problem
Solar.
Herro! Sycamore School will win National Science Bowl this year!!!
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