Answer:
Volume = 6783.27inch³
H = 6.951inch
L = 51.098inch
W = 19.098inch
Step-by-step explanation:
From the given information:
Let h = side length and height of the box
L = length of the box
W = width of the box
V = volume of the box
We have that:
L = 65-2h
W = 33-2h
V = L×W×h
Therefore we have
V = (65-2h)(33-2h)×h
V = (2145-130h-66h+4h²)×h
V = 2145h-196h²+4h³
By differentiating V w.r.t h, we have
V' = 2145-392h+12h²
V = 12h²-392h+2145
Using Almighty formula we have
h = 392+/-√392²-4(12)(2145)/2(12)
h = 6.951 or 25.716
Thus, we find L,W and V.
We use the least value of h in order not to get a negative value of volume, length and width
L = 65-2h = 65-2(6.951) = 51.098
W = 33-2h = 33-2(6.951) = 19.098
V = LWH = 51.098×19.098×6.951 = 6783.2696inches
