SOLUTION: A closed tank is to be made of sheet iron.it must have a square Base and sides perpendicular to the base. Its capacity is to be 8 cubic metres.find the length of the sides of the s

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Question 1056002: A closed tank is to be made of sheet iron.it must have a square Base and sides perpendicular to the base. Its capacity is to be 8 cubic metres.find the length of the sides of the square base and depth of the tank, so that the least amount of sheet iron may be used. Hint let the base =x and the height=h
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A closed tank is to be made of sheet iron.
it must have a square Base and sides perpendicular to the base.
Its capacity is to be 8 cubic metres.find the length of the sides of the square base and depth of the tank, so that the least amount of sheet iron may be used.
Hint let the base =x and the height=h
The vol equation
x * x * h = 8
x^2*h = 8
h = 8%2Fx%5E2; use this form for substitution
:
A closed square base box has 2 ea x^2 sides and 4 ea x*h sides
Surface area equation
S.A. = 2x^2 + 4xh
Replace h with 8%2Fx%5E2
S.A. = 2x^2 + 4x8%2Fx%5E2
cancel x
S.A. = 2x^2 + 4*8%2Fx
S.A. = 2x^2 + 32%2Fx
:
Plot this equation
+graph%28+300%2C+200%2C+-2%2C+8%2C+-10%2C+40%2C+2x%5E2%2B%2832%2Fx%29%29+
minimum surface area occurs when x = 2 which is 24 sq/m
h = 8%2F2%5E2
h = 2
A perfect cube 2 by 2 by 2, for least amt of sheet iron