## Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

# not much of a brain teaser...but

### #1 titambu

titambu

Newbie

• Members
• 1 posts

Posted 04 October 2007 - 12:37 AM

This has given me a headache!

Anyone can post some kind of ratio -formula- for dividing the VOLUME of an isosceles pyramid into 3 EQUAL sections (cut horizontally)???

I reeeeeally need this.

• 0

### #2 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 20 November 2007 - 08:47 PM

Let the height - apex to base - of the original pyramid be c.
Cut the pyramid with a plane parallel to the original base a distance b from the apex.
This defines a second pyramid with height b.
Cut again, a distance a from the apex. This defines a third pyramid, of height a.

Volume of any pyramid is proportional to the product of base area and height [1/3 i think - doesn't matter]

Area of pyramid bases is proportional to the square of their heights
So, volume of pyramids is proportional to cube of their heights.

You want the pyramid volumes to be in the ratio of 1[a] : 2(B) : 3[c]
so that the slices will have equal volumes.

a[cubed] = 1/2 b[cubed] = 1/3 c[cubed].

That should give you the ratios you need.

Caveat, I did this on the fly, and I'm only half awake,
so maybe some other genius will come along and correct this.

• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users