Please show step by step of working out the value of r for which is A minimum and calculate the minimum surface area of the container. The total surface area, Acm^2, of each container is modelled by function A= πr^2+100/r.

(remember to use the derivative to show you have found the minimum)

A = 59.63cm^2

Step-by-step explanation:

You have the following function for the surface area of the container:

               (1)

where r is the radius of the cross sectional area of the container.

In order to find the minimum surface are you first calculate the derivative of A respect to r, to find the value of r that makes the surface area a minimum.

        (2)

Next, you equal the expression (2) to zero and solve for r:

Finally, you replace the previous result in the equation (1):

The minimum total surface area is 59.63cm^2

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi