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anonymous
 5 years ago
A cylindrical can is to hold 1/2 cup of tomato sauce. What are the dimensions of its diameter and height in centimeters, to minimize the amount of metal to make the can?
V=(pi*d^2*h)/4
A=(pi*d^2)+pi*d*h
1qt=946cc
anonymous
 5 years ago
A cylindrical can is to hold 1/2 cup of tomato sauce. What are the dimensions of its diameter and height in centimeters, to minimize the amount of metal to make the can? V=(pi*d^2*h)/4 A=(pi*d^2)+pi*d*h 1qt=946cc

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is a tricky one....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1are thos answers? or formulas to apply?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0formulas it's a related rates question

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1yes, optimizations and such

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes they want D, H, and Amin

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1V = 1/2 cup, soo; .5 = (pi) (r^2) (h) right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1A = 2 circles and a rectangle :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1A = 2pi (r^2) + h(2pi r)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1use the volume to calibrate either h or r h = .5/pi r^2 seems easiest right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1substitute that "value" into the Area formula and then derive

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which value the 946cc?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1the .5 cups...worry about conversions afterwards

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1so...\[h = \frac{1}{2\pi r^2}\] right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1A = 2pi (r^2) + h(2pi r) sooo \[A = 2\pi r^2 + \frac{2\pi r}{2\pi r^2}\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1\[A = 2\pi r^2 + {1 \over r}\] correct?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1now derive :) you know how to derive?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1A = 4pi r  1/r^2 then correct?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes that is what I just got

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1if we combine these with like denoms we get: \[A'=\frac{4\pi r^3  1}{r^2}\] correct?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1\[A'=0=4pir^3 1\] so what are the zeros?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1r = ? the easiest way is to plug this into wolframs site and itll tell us right away ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay and the equation that I would type in would be \[\sqrt[3]{1/4\pi}\] right

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.14pi r^3  1 :) and i got abt .4 as the only root

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh okay you don't have to get r by itself

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1not with wolframs site; itll do it for you

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay and r^2 is the diameter and I can use that to solve for Amin

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1Yes; or simply use it to solve 'h'

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah I guess that would be easier lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1how many cups to a quart? 8 or 4?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.14 cups to 1 quart and we need half a cup so 1/8th of a quart right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.11/2 cup = 946/8 = 118.25 centimeters squared (cc) then

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.12 = abt 2.1 centimeters then

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1r = abt. 2.1 centimeters

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1A = 2pi(2.1)^2 + 1/(2.1)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1Total min area = 28.18 cc

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wouldn't it be 2.1^4 since it was d^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh never mind I see it now

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1diameter = 2r = 2(2.1) = 4.2 V = 128.25 = 2pi(2.1)^2 * h 128.25  = h = abt. 4.63 2pi (2.1)^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank you very much I've been working on this problem for about 3 hours and you figured it out in 10 minutes lol! You're a lifesaver!

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1is it right? cuase i might see an error in it; i allowed the area of the material to be 2 circles, top and bottom of a can; and a height...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes it is it matches up to the parts that I had figured out
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