SOLUTION: a tank is used to collect rain water.The form of the tank is a parallelepiped rectangle whose basement is a square whose side is x meters.its volume is 4 cubed meters Find the alt

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Question 1101986: a tank is used to collect rain water.The form of the tank is a parallelepiped rectangle whose basement is a square whose side is x meters.its volume is 4 cubed meters
Find the altitude of the tank
Find the surface in terms of x
Find the dimensions of the tank if we want to use as less paint as possible
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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a tank is used to collect rain water.
The form of the tank is a parallelepiped rectangle whose base is a square whose side is x meters.
its volume is 4 cubic meters
:
Find the altitude of the tank
let h = the height of the tank
x*x*h = 4
x^2 * h = 4
h = 4%2Fx%5E2
:
Find the surface in terms of x
Assuming the top is open
S.A. = x^2 + 4(xh)
replace h with 4%2Fx%5E2
S.A. = x^2 + 4(x*4%2Fx%5E2)
cancel x
S.A. = x^2 + 4(4%2Fx)
S.A. = x^2 + 16%2Fx
Find the dimensions of the tank if we want to use as less paint as possible
Find the minimum surface area by plotting the equation. Y = surface area
y = x^2 + 16%2Fx
+graph%28+300%2C+200%2C+-2%2C+5%2C+-10%2C+30%2C+x%5E2%2B%2816%2Fx%29%2C+12%29+
minimum occurs when x = 2 meters, therefore the dimensions are 2 by 2 by 1 meters with a surface area of 12 (greenline)