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279) A body is formed by a straight circular cylinder which ends up in a hemisphere. What are the dimensions that should have this body so the total surface area is minimal, if your volume is

answer Cubic sqrt( 3V/5 pi)

i tried to post an image of my notes and i couldnot i will type later

Vt = pir

A= 2pirH+ 2pir

Derive implicit 2piH + pir(dH) + 4pir

dh = (-2r-h)/(r)

derive volume 2pirH + pir

2pirH + pir

And I got piRh = 0

So h = 0 and this is not the answer

answer Cubic sqrt( 3V/5 pi)

i tried to post an image of my notes and i couldnot i will type later

Vt = pir

^{2}H +2/3piR^{2}constantA= 2pirH+ 2pir

^{2}Derive implicit 2piH + pir(dH) + 4pir

dh = (-2r-h)/(r)

derive volume 2pirH + pir

^{2}(dH) + 2pir^{2}2pirH + pir

^{2}(-2r-h) + 2pir^{2}= 0And I got piRh = 0

So h = 0 and this is not the answer

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