Hot Water Cylinder Differentiation

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Anonymous Poster	Hot Water Cylinder Differentiation 05/28/2010 5:59 PM
	Hi, I need help with a calculus qestion To reduce heat loss, the surface area of a hot-water tank must be kept to a minimum. If such a tank is 125 litters in capacity, and can be approximated by a cylinder in shape with a hemispherical end cap; calculate the radius and overall height for minimum heat loss. This is how far I've gotten: The volume is the sum of the volume of a hemisphere and a cylinder. The surface area is = Isolate h in the Volume equation. Substitute for h into the Surface area equation.
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lyn Guru Join Date: Oct 2008 Posts: 42355 Good Answers: 1693	#1 Re: hot water cylinder differentiation 05/28/2010 7:52 PM
	Don't have much, do ya? Why not delete the, "cylinder in shape" and use two hemispheres joined at the middle?
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Bill Guru Join Date: Dec 2005 Location: Clemson, South Carolina Posts: 1722 Good Answers: 18	#4 In reply to #1 Re: hot water cylinder differentiation 05/29/2010 5:17 AM
	Ya think he might "get" that you're trying to steer him in the right direction, if that's "all he's got?" __________________ We have met the enemy and he is us . . . Walt Kelly
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Shawn Power-User Join Date: Apr 2005 Location: Averill Park, NY Posts: 250 Good Answers: 4	#2 Re: Hot Water Cylinder Differentiation 05/28/2010 8:28 PM
	Two geometrical shapes must be taken into consideration. and if there are two end caps it is that of a circle and a cylinder. solve for h in terms of r in the volume equation, and use substitution in the second equation. then solve for r in the surface area equation. find when the first derivative of that equation is equal to 0. then you should find your answer. __________________ "There isn't a scientific community. It's a culture. It is a very undisciplined organization." ~ Francois Rabelais
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Tornado Guru Join Date: May 2009 Location: Richland, WA, USA Posts: 21017 Good Answers: 795	#3 Re: Hot Water Cylinder Differentiation 05/29/2010 12:25 AM
	If h is the height of the cylindrical part, then h = 0; if h is the overall height, then h = 2r. It depends on sorting out that ambiguity. (This is just another way of saying lynlynch's GA.) __________________ In vino veritas; in cervisia carmen; in aqua E. coli.
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PWSlack Guru Join Date: Jan 2007 Location: In the bothy, 7 chains down the line from Dodman's Lane level crossing, in the nation formerly known as Great Britain. Kettle's on. Posts: 32175 Good Answers: 839	#5 Re: Hot Water Cylinder Differentiation 07/10/2024 6:49 AM
	A sphere about twice the diameter of a soccer football fits the minimum surface-to-volume criterion; no calculus needed. No mention of insulation or windspeed... __________________ "Did you get my e-mail?" - "The biggest problem in communication is the illusion that it has taken place" - George Bernard Shaw, 1856
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Bill (1); lyn (1); PWSlack (1); Shawn (1); Tornado (1)

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