Question

You are to design an open-top rectangular stainless-steel vat. It is to have a square base and a volume of 32ft^3. What dimensions would have the least material needed?

Answer 1

x = side of square
y = depth
volume of open vat, V = x^2 y = 32 -------------- (1)

to qualify the statement "to weigh no more than necessary means that the surface area (S) of plate = minimum

S = x^2 + 4xy
using (1)
S = x^2 + 4x (32/x^2) = x^2 + 128/x
dS/dx = 2x - 128/x^2 = 0 for minimum
2x^3 = 128
x^3 = 64 = 4^3
x = 4 ft
y = 32/16 = 2 ft >>>>>>>> from (1)

the dimensions are x = 4 ft of base side
y = 2 ft as depth

Answer 2

;-; i didnt even get medal <\3

Answer 3

@Elsa213 Now you got a medal :P

Answer 4

:D tank chu (~;u;~)

Answer 5

:)
So at least there has been 2 people who have stalked @Luigi0210 's question ;P