Asked by Nancu
A box has a Square base. The Perimeter of the base plus the height is 120cm. What is the max volume of this box, and what are the dimensions of the this maximized box.
Answers
Answered by
Reiny
let the base be x by x cm
let the height be y
given: 4x + y = 120
y = 120 - 4x
V = x^2 y = x^2(120-4x)
= 120x^2 - 4x^3
dV/dx = 240x - 12x^2 = 0 for a max of V
12x^2 - 240x = 0
12x(x- 20) = 0
x = 0 ----> yields a minimum volume
or
x = 20
so the box is 20 cm by 20 cm by 40 cm for a max volume of 16000 cm^3
let the height be y
given: 4x + y = 120
y = 120 - 4x
V = x^2 y = x^2(120-4x)
= 120x^2 - 4x^3
dV/dx = 240x - 12x^2 = 0 for a max of V
12x^2 - 240x = 0
12x(x- 20) = 0
x = 0 ----> yields a minimum volume
or
x = 20
so the box is 20 cm by 20 cm by 40 cm for a max volume of 16000 cm^3
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.