Differentiation question

"A cylindrical can with height h metres and radius r metres has a capacity of 2 litres.
Find an expression for the surface area of the can in terms of r only."

I worked this out to be 2(pi)r^2 + 4.

The next part says "Find the value of r which minimises the surface area of the can."

I'm not even sure what that means. Do they want the smallest possible surface area? I also tried solving it like a quadratic, but it came up with a negative root.

Thanks in advance!

These types of questions are optimisation questions if you want to find explanations online somewhere. May be helpful if you're not sure what to search.

"A cylindrical can with height h metres and radius r metres has a capacity of 2 litres.
Find an expression for the surface area of the can in terms of r only."

I worked this out to be 2(pi)r^2 + 4.

The next part says "Find the value of r which minimises the surface area of the can."

I'm not even sure what that means. Do they want the smallest possible surface area? I also tried solving it like a quadratic, but it came up with a negative root.

Thanks in advance!

inb4 he types 'optimisation problems' on Google and comes up with Lagrange multipliers and complex methods.

$A = 2\pi r^2 + 4$ (assuming that's correct).

What's $\displaystyle \frac{dA}{dr} = ?$ What happens when dA/dr = 0? You can then prove that it's a maximum or minimmum by checking the second derivative.

Thanks you (again).

How did you get 2(pi)r^2+4 for part i I got (pi)r^2h=2 so h=2/(pi)r^2 for ii A = 2(pi)rh 2(pi)r^2 substituting part I for h =4(pi)r/(pi)r^2 =4/r then A = 4/r +2(pi)r^2