>Surface-area-> SOLUTION: A cylindrical steel container, open up at the top, is to have a capacity of 24 cubic metres. The price of material used for the bottom of the container is $0.15 per square metre, and also t var visible_logon_form_ = false;Log in or register.Username: Password: Register in one straightforward step!.Reset your password if you foracquired it."; rerevolve false; } "> Log On

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Click right here to watch ALL troubles on Surface-areaConcern 1137932: A cylindrical metal container, open up at the height, is to have a capacity of 24 cubic metres. The expense of product supplied for the bottom of the container is $0.15 per square metre, and also the cost of the material offered for the curved component is $0.05 per square metre. Find the dimensions that will certainly minimise the cost of the product, and also therefore show the minimum expense is $2.64. Answer by greenestamps(10016)
(Show Source): You deserve to put this solution on YOUR website! This is an excellent problem for you to learn something from, if you do the work-related yourself. There is some nice calculus; and there is the majority of ugly arithmetic with expressions like cube root of pi.I will certainly outline a path to the solution of the trouble and hope you will certainly select to fill in the details. Or, undoubtedly an additional tutor will view the problem and offer you a full solution; and you deserve to usage that if you don"t treatment to obstacle yourself to fix the problem yourself.The volume of the cylinder is 24: (1)The location of the bottom of the cylinder is ; the location of the sides is .With the product for the bottom of the cylinder costing $0.15 per square meter and also the product for the sides costing $0.05 per square meter, the cost of producing the cylinder is (2)Steps for you to take:1. Solve equation (1) for h in terms of r2. Substitute right into equation (2) to provide you a price attribute in regards to r just.3. Find the derivative of the expense attribute.4. Set the derivative equal to 0 and solve to find the worth of r that minimizes the price.So you deserve to examine your work, I will certainly tell you that the value of r that minimizes the cost isNext off action for you:5. Find an expression for h by substituting this value of r in the equation from step 1. above.I will tell you that the expression for h is incredibly similar to the expression for r, having actually a continuous in the numerator and a cube root of pi in the denominator.Last step:6. Evaluate the price attribute for the worths of r and h you have actually discovered.With both r and h having the form of a consistent split by the cube root of pi, both terms in the expense function (equation (2) above) will be of the develop some constant times the cube root of pi.

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When evaluated, that minimum value of the price feature is indeed $2.64 as soon as rounded to the nearemainder cent.