An aluminum can is to be constructed to contain 2400 cm3 of liquid.
Let r and h be the radius of the base and the height of the can respectively.
a) Express h in terms of r. (If needed you can enter π as pi.)

h=

b) Express the surface area of the can in terms of r.

Surface area =

c) Approximate the value of r that will minimize the amount of required material (i.e. the value of r that will minimize the surface area).
What is the corresponding value of h?

r=
h=

Question

An aluminum can is to be constructed to contain 2400 cm3 of liquid. 
Let r and h be the radius of the base and the height of the can respectively.
a) Express h in terms of r. (If needed you can enter π as pi.)

h= 

b) Express the surface area of the can in terms of r.

Surface area = 

c) Approximate the value of r that will minimize the amount of required material (i.e. the value of r that will minimize the surface area). 
What is the corresponding value of h?

r=  
h=

radar · Answer

Volume V = pi r^2 h   and Volume = 2400 cm^3
2400cm^3=pi r^2 h
h = (2400)/(pi r^2) =764/r^2
That is part a.  b. is same process except use formula for Surface Area

radar · Answer

Surface Area SA= 2 pi r h + 2 pi r^2  includes the circular bases

anonymous · Answer

oh thanks

radar · Answer

Substitute the value you obtained in part a. for h in the surface area.  Then use derivative to solve for r.

radar · Answer

S = 2 pi r (764/r^2) + 2 pi r^2     now do dS/dr    make that equal zero then solve for r.

radar · Answer

Look at dumbcow solution for a similar problem. http://openstudy.com/study#/updates/4e376c520b8bf47d065ed7f6