optimization problem calculus - XP Math - Forums

 XP Math - Forums optimization problem calculus

 11-26-2006 #1 Lili2000 Guest   Posts: n/a optimization problem calculus I have a hard time with an optimization problem. Any help is much appreciated. Problem: A Yuppie from Yorkville wishes to build a whirlpool in the renovated loft. The whirlpool will be cylindrical in shape and will hold 5m cube of water. The bottom of the pool will be ceramic tile and the sides will be redwood. Ceramic costs twice as much as the wood. Find the dimensions of the pool to minimize the cost of construction.
 11-27-2006 #2 Mr. Hui     Join Date: Mar 2005 Posts: 10,609 Start with the formula for the surface area and volume of a cylinder. $SA = 2{\pi}rh+2{\pi}r^2$ $V = {\pi}r^2h$ It holds 5m3 of water, so ${\pi}r^2h = 5$ and $h = \frac{5}{{\pi}r^2}$ $SA = 2{\pi}r({\frac{5}{{\pi}r^2}})+2{\pi}r^2$ $S(r) = SA = {\frac{10}{r}}+2{\pi}r^2$ $S'(r) = SA' = -{\frac{10}{r^2}}+4{\pi}r$ ${\frac{10}{r^2}} = 4{\pi}r$ $4{\pi}{r^3} = 10$ $r = \frac{\sqrt[3]{2.5}}{\sqrt[3]{\pi}}$ Use the $r$ to find the $h$ resulting in a cylinder with the smallest possible surface area. __________________ Do Math and you can do Anything! Last edited by Mr. Hui; 11-27-2006 at 09:14 PM..
 11-27-2006 #3 Sillysidley   Join Date: Oct 2006 Posts: 822 ??????????? What grade level is this supposed to be? I could probably do it ( in like an hour...), but i will probably get it wrong __________________ .
 11-27-2006 #4 Mr. Hui     Join Date: Mar 2005 Posts: 10,609 Calculus is most often a (required) college level mathematics course. It is also offered in high schools as Advanced Placement. This particular example deals with 3-D optimization, a topic usually covered in an advanced calculus course. __________________ Do Math and you can do Anything!
 11-28-2006 #5 kickonlanky Guest   Posts: n/a that stuff looks and i know it is, HARD. WUT GRADE IS LILI2000 IN??? is she insane doing this kind of work
11-28-2006   #6
Sillysidley

Join Date: Oct 2006
Posts: 822

Quote:
 Originally Posted by kickonlanky that stuff looks and i know it is, HARD. WUT GRADE IS LILI2000 IN??? is she insane doing this kind of work
U will probably have to do this kind of stuff too later
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 11-28-2006 #7 Sillysidley   Join Date: Oct 2006 Posts: 822 It sure is __________________ .
 11-28-2006 #8 Sillysidley   Join Date: Oct 2006 Posts: 822 trig isn't too hard... __________________ .
 11-28-2006 #9 Mr. Hui     Join Date: Mar 2005 Posts: 10,609 Trig is hard. It's mostly memorization of the sin, cos and tan functions. __________________ Do Math and you can do Anything!
 11-28-2006 #10 Sillysidley   Join Date: Oct 2006 Posts: 822 what is the correct name of that circle with a ine through it? It can be used in the equation s=r(the circle thin) it is the central angle, but waht is the correct name? __________________ .

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