Find the dimensions of a right-circular cylinder that is open on the top and closed on the bottom, so that the can holds 1 liter and uses the least amount of material? ... ?

Volume of cylinder:

V = πr²h

The desired volume is 1 Liter = 1000 cm³

1000 = πr²h

h = 1000/πr²

Surface area of cylinder:

S. A = 2πr² + 2πr²h

We substitute the value of h from the first equation:

S. A = 2πr² + 2πr (1/πr²)

S. A = 2πr² + 2/r

Now, to minimize surface area, we differentiate the expression with respect to r and equate to 0.

0 = 4πr - 1000/r²

4πr³ - 1000 = 0

r = 4.3 cm

h = 17.2 cm