Question 1125333
Original Poster here and I got it already so no worries! Heres the work.

Let x = the side of the square base and y = height
Let V = volume = x2y
The surface area = 2x2 + 4xy = 121.5
 
Solve surface area equation for y = (121.5 - 2x2)/4x and sub this into the volume equation
 
V = x2(121.5 - 2x2)/4x = x(121.5 - 2x2)/4
  
derivative of V with respect to x = (x/4)(-2x) + (1/4)(121.5 - 2x2) = 0 at the maximum
 
(1/4)(-4x2 + 121.5 - 2x2) = 0
6x2 = 121.5
x2 = 20.25
x = 4.5
y = (121.5 - 40.5)/(4 * 4.5) =81/18 = 4.5 -> max volume with side 4.5