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August 30, 2014

August 30, 2014

Posted by **ibranian** on Tuesday, August 7, 2012 at 1:35pm.

- math -
**Reiny**, Tuesday, August 7, 2012 at 2:19pmI assume we are not worried about the base of the silo.

So we need the "sleeve" of the silo plus a hemisphere

let the radius be of the hemisphere be r ft and the height of the cylinder part be h ft

surface area (SA) = 2πrh + (1/2)4πr^2

Cost = 1(2πrh) + 2(1/2)4πr^2

= 2πrh + 4πr^2

but πr^2 h + (1/2)(4/3)πr^3 = V , where V is a constant

h = (V - (2/3)πr^3)/(πr^2)

sub that back into Cost = ....

simplify, then take the derivative

set that equal to zero and solve for r

Make sure you treat V as a constant.

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