A closed-top cylindrical container is to have a volume of 250 in2. 250 , in squared , . What dimensions (radius and height) will minimize the surface area?

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

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50