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In this question, a factory produces cylindrical cans without lids.
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The materials used in the curved part are three times more expensive than the bottom parts.
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The cans should have a volume of one decameter being cubed.
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And i want to know what height and radius should give the cheapest cans to produce.
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So we have these cylindrical cans that don't have lids.
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So now the volume of a cylinder is pi r squared times the height.
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And that's going to be equal to one.
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Now we are trying to minimize the cost.
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And what is the cost? well for the curved part, it costs three times more money than the bottom.
00:51
So now the area of the curved part, the lateral area of a cylinder, is two pi r h.
01:00
So i'm going to have three times that two pi r h.
01:05
And to that, i'm going to add the cost of the bottom.
01:10
The cost of the bottom is pi r squared.
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So now, since i know that pi r squared h is equal to one, i can solve for the h.
01:21
I can say that my h is equal to one over pi r squared.
01:27
And i'm going to plug that in.
01:29
So my cost is six pi r times one over pi r squared plus pi r squared.
01:40
Now in my first term, the pi's, they cancel.
01:43
The r's, they cancel...