What should the dimensions of a cola bottle be if we wanted to minimize the cost of producing it while retaining the volume of 355mL?
2007-01-31 05:13:21 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Engineering
Bottle is like a can.
2007-01-31 06:22:29 · update #1
The bottle is cylindrical.
2007-01-31 06:23:32 · update #2
If you assume that production costs include material costs and are not dependent on the shape of the bottle, then what you'd want to do is minimize the mass of plastic used while maintaining an internal volume of 355 ml. For a constant thickness, that means you want to minimize the surface area.
What is your geometry? Block, cylinder, sphere? You didn't say. If your thickness is constant, the least surface area per unit volume is obtained with a perfect sphere. Obviously, spheres don't make very good bottles. A next best approach is for the bottles to be cylindrical instead of rectangular.
2007-01-31 05:25:21 · answer #1 · answered by . 4 · 0⤊ 0⤋
The volume of a cylinder is V = h*r^2*pi, The surface area is A = h * 2 * pi * r + 2 * pi * r^2
Solve the Volume equation for h (you already know V) and substitute for h in the Area equation so that the equation only has the r variable. Now find the r for the minumum Area by setting the derivative of that equation to zero and solving for r.
You can do it!
2007-01-31 08:05:49 · answer #2 · answered by rscanner 6 · 0⤊ 0⤋
To many people do not understand that the biggest cost in producing many things is labor cost and not material cost. An unconventional production process can save on material but increase labor and equipment costs.
2007-01-31 16:31:20 · answer #3 · answered by Stan the Rocker 5 · 0⤊ 0⤋
V=355 mL,,,,, the minimum shape is sphere or a ball shape.
V= (pi) r^3 4/3,,,,,,,,,,,,,355= 3.14 r^3 4/3,,, 113=r^3 1.33
84.81 =r^3 ,,,,,,,,,r=4.4 cm radius
2007-01-31 06:02:54 · answer #4 · answered by Anonymous · 0⤊ 0⤋