SOLUTION: An open square based container is to be made with a volume of 144 cm cubed. Calculate the exact dimension of the box if the surface area of the box is to be minimum.

Algebra ->  Trigonometry-basics -> SOLUTION: An open square based container is to be made with a volume of 144 cm cubed. Calculate the exact dimension of the box if the surface area of the box is to be minimum.       Log On


   

Question 990661: An open square based container is to be made with a volume of 144 cm cubed. Calculate the exact dimension of the box if the surface area of the box is to be minimum.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the measure of the side of the square bottom of the box. Let represent the height of the box.

The volume of the box is , so solving for , we get

The surface area of an open box is the area of the 4 sides, plus the area of the bottom,

So, the surface area as a function of the height of the box is:





Set the derivative equal to zero and solve for , then use .

John

My calculator said it, I believe it, that settles it