# math

posted by .

Your iron works has been contracted to design and build a 500-ft3 square-based, open-top, rectangular steel holding tank for a paper company. The tank is to be made by welding half-inch-thick stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible. What dimensions do you tell the shop to use?

• math -

clearly the weight of the box is a function of the material used, which in turn depends on the surface area of the sheet metal used.
So we want a minimum surface area.
let each side of the base be x ft, and let the height be y ft.
Area = x^2 + 4xy
but x^2 y = 500
y = 500/x^2

area = x^2 + 4x(500/x^2) = x^2 + 2000/x
d(area)/dx = 2x -2000/x^2 = 0 for a min of area
2x = 2000/x^2
x^3 = 1000
x = 10 , then y = 500/10^2 = 5

the box should have a base of 10 ft by 10 ft, and a height of 5 ft.

## Similar Questions

1. ### Stainless Steel

How sharp is stainless steel? Can someone give me a comparsion to how sharp stain steel is?
2. ### Calculus (optimization problem)

A cyclinderical tank with no top is to be built from stainless steel with a copper bottom. The tank is to have a volume of 5ð m^3. if the price of copper is five times the price of stainless steel, what should be the dimensions of …
3. ### Calculus AB/AP

A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4 meters and its volume is 36 cubic meters. If building the tank costs \$8 per square meter for the base and …
4. ### Physics

Assume you construct a new water tower for a town water supply. Assume the tank is in the shape of a sphere with a diameter of 21ft. Assume the tank is made of formes and welded .5 in steel plate that weighs 150 lb per ft3. What is …
5. ### math

An open steel tank measures 2m by 2.5m by 3m.It holds 7500 ml of water. What is the volume of steel,in cubic metres,making up the sides of the tank ?
6. ### math

an open steel tank measures 2m by 2.5m by 3m.It holds 7500 ml of water.What is the volume of steel,in cubic metres,making up the sides of the tank ?
7. ### Calculus

Bruce has commissioned the construction of an open-top rectangular tank to be fashioned from a 3m by 5m sheet of steel. Squares will be cut from each corner and sides will be bent upward to form the tank to be used for live bait storage. …
8. ### Physics

A 16.0 gallon steel tank is topped off with gasoline at 0 degrees C. With the lid off, the tank is left outside where the air temp is a sizzling 40.0 deg C. How much gasoline overflows?
9. ### chem

A piece of stainless steel (Sstainless steel = 0.50 j/g* C) is transferred from an oven (180 *C) to 125mL of water in an insulated container at 23.2 *C. The water temperature rises to 51.5 *C. What is the mass of the stainless steel?
10. ### Calculus

A rectangular tank with a square​ base, an open​ top, and a volume of 4,000 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. I'm not understanding how to get started …

More Similar Questions