Answer:
radius r = 3.414 in
height h = 6.8275 in
Step-by-step explanation:
From the information given:
The volume V of a closed cylindrical container with its surface area can be expressed as follows:


Given that Volume V = 250 in²
Then;

We also know that the cylinder contains top and bottom circle and the area is equal to πr²,
Hence, if we incorporate these areas in the total area of the cylinder.
Then;



To find the minimum by determining the radius at which the surface by using the first-order derivative.




![r =\sqrt[3]{39.789}](https://tex.z-dn.net/?f=r%20%3D%5Csqrt%5B3%5D%7B39.789%7D)
r = 3.414 in
Using the second-order derivative of S to determine the area is maximum or minimum at the radius, we have:


Thus, the minimum surface area will be used because the second-derivative shows that the area function is higher than zero.
Thus, from 

h = 6.8275 in