Question

What is the minimum surface area of a box whose top and bottom is a square if the volume is 40 cubic inches. (Surface area is the area of all the sides of the box).

Answer 1

let length of box is x

width of the box is x

height of the box is y

Volume of the rectangular box

V=length*width*height

V=x^2y

40=x^2y

y=40/x^2 ------------(1)

surface area of the box

  

----------(2)

Differentiating with respect to x

for critical points

second derivative

at

so is minima points

from equation (1)

from equation (2)