Maximize volume of a pyramid cut from piece of paper.
Not what you're looking for?
(Problem) A pyramid consists of 4 isosceles triangles around a square base. If this is to be cut and folded out of a single square piece of paper, Maximize the volume.
h=height of pyramid
x=one side of base square
P=length(or width) of paper
I know... V=x^2(h/3)
h=sqrt((x/2)^2+something^2)
h=sqrt((P/2)^2+something else^2)
I know I need to get volume in terms of one variable, take the derivative and find the max point of that curve. I understand that as x gets larger, h gets smaller, but my geometry isn't strong enough to find the actual relationship between all these things.
What the heck is the equation for the volume in terms of one variable?
Purchase this Solution
Solution Summary
The expert maximizes volume of a pyramid cut from piece of paper.
Solution Preview
Above two figs. are self explanatory.
_
Diagonal CB = √2 P
EF = b (side length of the base of the pyramid)
_
BF = (CB - EF)/2 = (√2 P - b)/2
...
Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Probability Quiz
Some questions on probability
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.