A pyramid whose altitude is 5 feet weighs 800lbs . At what distance from its vertex must it be cut by a plane parallel to its base so that the two solids of equal weight will be formed?

i have no idea how to solve this

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- Dec 3rd 2011, 10:11 AMTechnicianEngineerSolid Geometry
A pyramid whose altitude is 5 feet weighs 800lbs . At what distance from its vertex must it be cut by a plane parallel to its base so that the two solids of equal weight will be formed?

i have no idea how to solve this - Dec 3rd 2011, 11:02 AMprincepsRe: Solid Geometry
- Dec 3rd 2011, 11:49 AMearbothRe: Solid Geometry
1. I assume that the material of the pyramid is homogenous. Then the weight correspond directly to the volume:

where k is a real constant.

2. denotes the base area of the complete pyramide, b the base area of the smaller pyramide. Both areas are similar. Then

with

3. h denotes the height of the smaller pyramid. Then the volume is calculated by:

with

4. Since and are similar you can use the proportion:

5. Plug in this term into the equation at #3:

Solve for h.