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 = 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