If 4,800 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Step 1 Let b be the length of the base and h the height. Then we must maximize the volume of the box, V

32000cm^3

Explanation:

Length L be base length

h be the height

Volume=V

V=L^2h

Surface area if box = L^2+4lh=4800

Solving for h

(4800-l^2/4L) = h

1200L-L^3/4=h

Substitute for h in V = L^2h

v=1200L-L^3/4

Differenting = 1200-3*L^2/4=0

L=√ (1600) = 40

Substitute L=40

In V=1200L-L^3/4

Hence 1200*40-40^4/4=32000cm^3