Maximum volume

[Guest]

If the surface area of a square prism is 54 cm^2, find the dimensions of the prism which has maximum volume.

thanks in advance.

Geovanny Navarro-Bustos

 

[Gene]

The sides of the square are s.
The length = l.

The area = 2s² + 4sl = 54
The volume = s²l
Solve the first for l
Substitute for l in the second.
Take dv/ds = 0 and solve for s
Solve for l