Question

A cylindrical can is to be made to hold 355 mL (=355 cm^3) of soda drink. If we were going to be concerned solely with reducing the manufacturing cost, then we would like to find the dimension of the can that produces the smallest surface area while keeping the volume constant at 355 mL.

a) suppose the soda can has perfect cylindrical shape comprised of the top and bottom circular disks with radius 'r', and the side with height 'h'. Write down the volume V and surface area A of the soda can as a function of two variables: height 'h' and radius 'r'.

Answer 1

Hint:

Volume of Cylinder:
\[V = 2\pi r h\]

Surface Area of Cylinder:

\[SA = 2\pi r^2 + 2\pi rh\]

The volume of the cylinder is given. Find the Surface Area, then substitute it for SA

Answer 2

And make sure the surface area is the "smallest" possible.

Answer 3

b) use the constraint that the volume is fixed at 355 mL to rewrite the surface area A as a function of only one variable: radius 'r'

Answer 4

c) we choose a reasonable range for the radius r to be between 2cm and 5cm. Use the closed interval method to find the smallest surface area A.

d) what is the dimension of the soda can ('h' and 'r') when the minimal surface area is achieved

Answer 5

Oh, we get answer choices. That was nice of them.

Answer 6

I guess a) is definitely not it.

Answer 7

no, those are not answer choices, they are different parts of the question

Answer 8

I see :)

Answer 9

sooo, how do i go about solving the other parts........

Answer 10

We still have to complete the first part first.