The capacity of the box is 36000 cubic centimeters. Find the least materials used in making the box if the length is twice its width.

Answer 1

volume=h*l*w
l=2w
v=2hw^2 or w=sqrt(36000/2h)
v=36000
now for the materials...
area=2lw+2hw+2hl
=4w^2+2v/l +36000/w+ v/w^2*2w=2w^2+36000/w+72000/w
going to calculus
darea/dw=0=4w-36000/w^2-72000/w^2
0=4w^2-108000
w^2=27000
w=30 cm
then l=60cm
and h=36000/1800=20cm