How to Make Cisterns | Python Fiddle

"""
How to Make Cisterns
Our friend in the illustration has a large sheet of zinc, 
measuring (before cutting) eight feet by three feet, and he 
has cut out square pieces (all of the same size) from the four 
corners and now proposes to fold up the sides, solder the edges, 
and make a cistern. But the point that puzzles him is this: Has 
he cut out those square pieces of the correct size in order that 
the cistern may hold the greatest possible quantity of water? You 
see, if you cut them very small you get a very shallow cistern; 
if you cut them large you get a tall and slender one. It is all a 
question of finding a way of cutting put these four square pieces 
exactly the right size. How are we to avoid making them too small or 
too large?

"""
import math
vol=[]
maxvol=0
#the square cutouts can be a maximum of less than 1.5 feet  
h=range(1,150)  #have to be integers but will divide by 100
length=8
width=3
for height in h:
    height= height/100.0
    volume=(length-2*height)*(width-2*height)*height
    vol.append(volume)
    if volume>maxvol:
        maxvol=volume
        maxdata=[height,maxvol]
        
        
print 'height %2.2f feet for max volume of %3.2f cubic feet' %(maxdata[0],maxdata[1])

a=3
b=8
print 'From answer in book ' + str(round(( a + b - math.sqrt(a**2 + b**2 - a*b))/6.0,2))+' feet'

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