An industrial tank (shape: a solid formed by adjoining two hemispheres to the ends of a right circular cylinder) must have a volume of 3000 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that will minimize cost.
Finding dimensions that will minimize cost~ please help
- Thread starter roxstar1
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The length of the cylindrical part is "h"; the radius of the cylindrical part and the two hemispherical parts is "r".
Use the cylinder-volume formula and the sphere-volume formula to find an expression for the total volume of the tank. Set this equal to the given total volume.
Solve this equation for one of the variables. (Solving for "h=" would probably be simpler.)
Now use the cylinder-surface-area formula and the sphere-surface-area formula (times "2")to find an expression for the total cost of the tank. Use your "solving" from above to substitute for the variable you solved for.
Now you have a "cost" formula in terms on only one variable. Minimize.
Eliz.
Use the cylinder-volume formula and the sphere-volume formula to find an expression for the total volume of the tank. Set this equal to the given total volume.
Solve this equation for one of the variables. (Solving for "h=" would probably be simpler.)
Now use the cylinder-surface-area formula and the sphere-surface-area formula (times "2")to find an expression for the total cost of the tank. Use your "solving" from above to substitute for the variable you solved for.
Now you have a "cost" formula in terms on only one variable. Minimize.
Eliz.