Answer to Question #311378 in Civil and Environmental Engineering for jam

Question

A rectangular box with a square base and no top is to have a volume of 108 cubic inches. Find the dimensions for the box that require the least amount of material.

Answer 1

volume = v = x^2 h

area = a = x^2 + 4 x h

h = 108/x^2

a = x^2 + 4 x (108/x^2)

a = x^2 + 432/x

da/dx = 0 = 2 x -432/x^2

432 = 2 x^3

x^3 = 216

x = 6

h = 108/36 = 3