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#1 2014-02-19 21:02:08

thedarktiger
Member
Registered: 2014-01-10
Posts: 91

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 ><
hmm 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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Registered: 2010-06-20
Posts: 10,058

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 smile

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#3 2014-02-19 21:15:20

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

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 smile

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#4 2014-02-20 21:36:55

thedarktiger
Member
Registered: 2014-01-10
Posts: 91

Re: stuff in a box

Yes thats it! thanks.


Good. You can read.

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#5 2014-10-25 12:28:50

SolarDevil
Member
Registered: 2014-09-14
Posts: 37

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!!! big_smile

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#6 2014-10-25 20:34:41

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

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 smile

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#7 2014-10-26 05:51:39

SolarDevil
Member
Registered: 2014-09-14
Posts: 37

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!!! big_smile

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#8 2014-10-26 20:35:52

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

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 smile

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#9 2014-10-28 11:48:12

SolarDevil
Member
Registered: 2014-09-14
Posts: 37

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!!! big_smile

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#10 2014-10-28 20:47:41

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

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 smile

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#11 2014-10-29 09:30:25

SolarDevil
Member
Registered: 2014-09-14
Posts: 37

Re: stuff in a box

Oh, I see. Thanks!


Herro! Sycamore School will win National Science Bowl this year!!! big_smile

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#12 2014-10-29 09:49:57

droid347
Member
Registered: 2014-10-29
Posts: 1

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
Member
Registered: 2014-09-14
Posts: 37

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!!! big_smile

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