Asked by mark
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.
Answers
Answered by
bobpursley
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
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
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