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anonymous
 one year ago
I need help visualizing this question. (Calc 1)
anonymous
 one year ago
I need help visualizing this question. (Calc 1)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0there was supposed to be an attachment

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0A metal through with equal semicircluar ends and open top is to have a capacity of 128pi cubic feet. Determine its radius r and length h is the trough is to require the least material for its construction.

triciaal
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433651448727:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the ends of the are semicircle are closed?

triciaal
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433651580013:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now just write an expression for the volume, Then one for the Surface area. Use the volume formula to turn the surface area formula into a single variable. Then Differentiate the last formula, set it equal to zero and solve. This will give you either h or r (depending on how you get on) Then substitute back into first formula to find the other variable.

triciaal
 one year ago
Best ResponseYou've already chosen the best response.2I see a cylinder split in half then turned on the side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I see a cylinder split in half too.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0volume of a cylinder/2= 128pi?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then 2h+4r+2pi(r)=perimeter of the trough?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2perimeter? hmm we're looking to minimize `surface area`, ya? :) remember how to find surface area of a cylinder?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the materials would be sum the dimensions of all the sides would it not?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2no, that would take care of the .. edges i suppose, not the surfaces though.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433648747657:dwFor a cylinder, we have two of these panels, one on top and one on bottom, ya? area of a circle is pi r^2. So to get the surface area of the top and bottom combined, we have 2pi r^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0SA of a cylinder= 2pi(r)h+ 2pi(r)^2

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Or you can jump right to your formula :) yah that's fine hehe.

triciaal
 one year ago
Best ResponseYou've already chosen the best response.2dw:1433652364767:dw

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Our trough will have exactly half of that surface area, so the formula we'll use is:\[\Large\rm A=\pi r^2+\pi r h\]I divided everything by 2 to cut it in half.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the cylinder volume formula would have to be cut in half as well?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2You're trying to minimize the area function. So eventually you want to get \(\Large\rm A'\) and set it equal to zero to look for `critical points`. But first, you want A in terms of ONE VARIABLE so it's easier to work with.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Yes, tric put the 1/2 in front of the pi r^2 h to show that :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2the Area formula is what we're trying to minimize, the volume formula is our constraint. It relates r to h. It allows us to make a substitution in our Area formula. Do you see how that will work? :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would isolate for h in the volume formula then sub it into the SA formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[SA \prime =4Pir(512\Pi/r ^{2})?\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Mmm that's what I'm coming up with also! yay

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, so when i originally tried to figure out the perimeter i was trying to get just the sides?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433649816855:dw

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2um um um :) ya perimeter gives us the distance across all of those edges i guess.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, thank you so much.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Were you able to find the corresponding height using that radial value? :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Remember that they want the radius `and` height that minimize the area :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[h= 256\div \sqrt[3]{128}^2\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2cool :) that will simplify a lil bit if you want both your height and radius in exact value,\[\Large\rm h=\frac{256}{(128)^{2/3}}=\frac{2\cdot128}{(128)^{2/3}}=2(128)^{1/3}\]
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