i need to make a soda can that fills up with 355ml. material A, used for only the top, costs 3 cents per square meter. material B, used for the side and the bottom, costs 5 cents per square meter. how would i start this?
2007-12-04 15:23:32 · 3 answers · asked by ? 3 in Science & Mathematics ➔ Engineering
Well its a simple calculus question really. Ask yourself. How can I maximize volume (335ml). While minimizing surface area. I would find the formula for the volume of the can. Take the derivative. Find the relative minimum (this will be your minimum surface area) while keeping your 335 ml for volume. Dont take my answer as fact. I know the first part is right but I reached some ambiguity as I attempted to figure out how to get the 335ml back into this minimized surface area.
2007-12-04 15:31:23 · answer #1 · answered by moonfinch 2 · 0⤊ 0⤋
Keep in mind (if this is not just a school math problem) that you don't have much choice on the diameter if it is going to be able to fit into a standard soda can vending machine or any other packaging machine or package size that has been standardized by the industry. It is a great question but may not produce an answer anyone could buy.
2007-12-05 00:18:44 · answer #2 · answered by Rich Z 7 · 0⤊ 0⤋
set up a function that determines the cost of the can
cost = (pi*r^2)*5 + (h*2*pi*r)*3
r is the radius in meters
h is the height in meters
within the parentheses are the respective areas
and minimize this subject to
volume = pi*r^2*h = 355 mL in m^3
you need to convert mL to m^3
solve for r and h
2007-12-04 16:17:14 · answer #3 · answered by . 5 · 1⤊ 0⤋