Acylindrical can is to be made to hold 1 l (1000 cm3 ) of oil. find the dimensions of the radius and height that will minimize the cost of the metal to manufacture the can. [hint: minimize a = 2πr2 + 2πrh subject to a constraint on the volume.]

r=5.42cm

h=10.83cm

Step-by-step explanation:

Hello!

To solve this problem please use the following steps, the complete procedure is attached.

1. Raise the equation for the volume of a cylinder and solve for the height (H)

2. Use the equation for the surface area of a cylinder, and replace the height using the equation found in step 1.

3. Derive the equation with respect to the radius and equal it to zero, then solve for the radius of the cylinder. Remember that the objective is to find that with the minimum surface area, the required volume is generated.

4. Once the radius is found, find the height with the equation from step 1

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)