a square based box is to be constructed such that its volume is exactly 1.5m^3. the following s guide you through the process of determining the base side length and box height such that the minimum amount of cardboard is used to construct the box.
a)
the equation for box volume can be used to express box height in terms of the side length of the base of the box. if the side length is denoted enter the function here
b)
use your result from part (a) to write a function for the surface area of cardboard used in the construction of the box. your function should be entirely in terms of the side length of the base of the box, x.
c)
to minimise the surface area of cardboard, we need the derivative of the surface area function with respect to x. this derivative is /=
d)
the minimum surface area will occur when the length of the sides of the box base is =
e)
finally, the height of the box must then be ℎ=