



 
Hi James, I agree with what you have done in developing expressions foe the volume and cost with one small change. You don't know the costs of the materials just that one material is twice as expensive as the other. Suppose that the material for the walls costs $k per square unit then the material for the hemisphere costs $2k per square unit. Then the cost of materials is
and the volume is
As you pointed out the challenge now is to express C as a function of one of the variables R and H and then differentiate, keeping in mind that k and V are constants. The key is the equation for the volume which can be written
and hence
Substitute this value for H in the expression for the cost and the cost then becomes a function of R alone. Penny  


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