Asked by nani
A closed cylindrical can is to hold 2 litter (200 cm³) of liquid. How should we choose the height and radius to minimize the amount of material needed to manufacture the can?
Answers
Answered by
Reiny
A litter is a group of kittens, a litre is a fluid measure of 1000 ml
let the height be h cm
let the radius be r cm
πr^2 h = 200
h = 200/(πr^2)
amount of material ---> surface area (SA)
SA = 2πr^2 + 2πrh
= 2πr^2 + 2πr(200/(πr^2))
= 2πr^2 + 400/r
differentiate, set that equal to zero, and solve for r
Plug back into h= ...
and you are done
let the height be h cm
let the radius be r cm
πr^2 h = 200
h = 200/(πr^2)
amount of material ---> surface area (SA)
SA = 2πr^2 + 2πrh
= 2πr^2 + 2πr(200/(πr^2))
= 2πr^2 + 400/r
differentiate, set that equal to zero, and solve for r
Plug back into h= ...
and you are done
Answered by
Temuulen
Radius=1.99735...
Height=3.984...
Height=3.984...
Answered by
Temuulen
I am sorry, I put wrong answer
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