Q: A cylinder of radius 16 and depth 20 is filled with silver ore. The cost of extracting the ore lying at a depth of h feet is 120(1+0.03h^2) dollars per cubic foot. How much will it cost to empty the entire cylinder?
I expect I will have to do some differentiation, I am just not quite sure how I do that in relation to the cylinder?
I expect I will have to do some differentiation, I am just not quite sure how I do that in relation to the cylinder?
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Integrate 120(1+0.03h^2) as
integral of 120 dh + integral of 120*0.03h^2 dh between the limits h=0 to h=20
to get cost per cubic foot as 12000
total volume=PI*16*16*20
total cost =12000*PI*16*16*20
=$193019453
integral of 120 dh + integral of 120*0.03h^2 dh between the limits h=0 to h=20
to get cost per cubic foot as 12000
total volume=PI*16*16*20
total cost =12000*PI*16*16*20
=$193019453