Question 192424
This is a practice problem for my daughter's upcoming state tests. We have a rectangular box measuring 12in. length, 8in. width and 3in. high. We calculated the volume to be 288 m3, and the surface area to be 312 m2. They are asking for us to find the dimensions of a box that has the same volume, but less surface area. 
:
A square box gives max volume; let x = the 3 dimensions; then
x^3 = 288
x = {{{288^(1/3)}}} use a calc
x = 6.604 would be very close (6.604^3 = 288.02)
:
Find the surface area of this box: 
SA = 2x^2 + 2x^2 + 2x^2
SA = 6x^2
SA = 6 * 6.604^2
SA = 261 sq in only