You are to place a sphere of ice cream into a cone with the height of 1.
a) What radius of the sphere will give you the most volume of ice cream inside the cone (as opposed to above the cone) for a cone with a base angle of 30 degrees?
b) What percent of this sphere of most volume lies inside the cone?
Things to consider:
This is essentially a complicated max/min problem, and a rather silly application of techniques that are very important in solving more realistic problems in which one needs to optimize some geometric relationship between unlike objects. You will find this project difficult because you will have to determine from sketches expressions involving more that one variable, and then compute with those expressions. In order to make progress, you will have to choose to let some of the variables act as parameters, at least temporarily.
If you would like a sketch of the drawing please email me... byers2008@yahoo.com
2007-02-28
03:50:13
·
3 answers
·
asked by
sweetness101010
1
in
Mathematics