What are the dimensions of the most economical cylindrical can?

[teng125]

A cylindrical can is to hold 20 m3. The material for the top and bottom costs
€10/m^2 and material for the side costs €8/m^2. Find the radius r and height h of
the most economical can.

the answer is h= 5 and j=2

i have found the eqn such as v=pi j^2 h =20 pi

and 2pi j^2 + pi j h = 18...then i don't know how to do...pls help

 

[berkeman]

Have you learned yet how to use differentiation to find maxima and minima of a function?

 

[teng125]

ya...but is my eqn correct??

 

[berkeman]

What's "j"? Where's "r" in the equations?

 

[teng125]

j = radius

 

[berkeman]

Well, anyway, I'd solve it this way:

-- write an equation 1 for V = f(r,h)

-- write an equation 2 for A = f(r,h)

-- rearrange equation 1 so you can substitute it into equation 2 to eliminate r in equation 2.

-- differentiate the result with respect to h, and set the result = 0

-- solve for the height h that minimizes the area, and then use equation 1 to solve for r.