Question
What are the dimensions of a closed rectangular box that has a square cross section, a capacity of 122 in.3, and is constructed using the least amount of material? (Round your answers to two decimal places.)
Answers
oobleck
the volume is v = x^2 y = 122, so y = 122/x^2
the surface area is
a = x^2 + 4xy = x^2 + 4x(122/x^2) = x^2 + 488/x
da/dx = 2x - 488/x^2
so now just find where da/dx=0.
the surface area is
a = x^2 + 4xy = x^2 + 4x(122/x^2) = x^2 + 488/x
da/dx = 2x - 488/x^2
so now just find where da/dx=0.