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Geometry in the Real World

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Corinne Mazurek

on 3 November 2013

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Transcript of Geometry in the Real World

Geometry in the Real World
Formulas
Perimeter (length around the shape): add the lengths of each side of the shape
Area (space inside a shape):
Square/Rectangle= length*width Triangle=.5*base*height Trapezoid=.5*(base1+base2)*height
Volume (space inside three dimensional shapes):
Cube=length*width*height Cylinder=Π(radius^2)height
Surface Area (space of an objects surface):
Rectangle=(2*length*height)+(2*width *height)+(2*width*length) Cylinder=2Π(radius^2)+2Π*radius*height
Maximize and Minimize
Optimization Problems
Relates Perimeter to the Area
Relates Surface Area to Volumes
Sources
Textbook and Notes
Fencing Problem: http://cims.nyu.edu/~kiryl/Calculus/Section_4.5--Optimization%20Problems/Optimization_Problems.pdf
Fencing
A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?
Can
You are designing a 1 Liter can. What dimensions (radius and height) will minimize the total amount of aluminum needed for this can?
Common Examples
Fencing and Area
Surface Area of a Can
(work through this problem on the board for the class)
(problem worked through on the board)
Full transcript