SOLUTION: the surface area of an open cylindrical tank is 68 square meter. If the diameter is 2/3 of its height, what is the height of the tank?

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Question 766746: the surface area of an open cylindrical tank is 68 square meter. If the diameter is 2/3 of its height, what is the height of the tank?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
d= diameter
h = height
d=(2/3)h, described as given
surface area with one side as the bottom but no top :
____Basic Formula_____pi%2A%28d%2F2%29%5E2%2B%282%2Api%2Ad%29h+
+pi%2A%28%282%2F3%29h%2F2%29%5E2%2B2%2Api%2A%28%282%2F3%29h%2F2%29

pi%2A%28h%2F3%29%5E2%2Bpi%2A%282%2F3%29h
pi%2A%28%28h%2F3%29%5E2%2B2h%2F3%29
pi%2A%28%281%2F9%29h%5E2%2B%282%2F3%29h%29

Surface area given is 68 m^2, so
pi%2A%28%281%2F9%29h%5E2%2B%282%2F3%29h%29=68
%281%2F9%29h%5E2%2B%282%2F3%29h=68%2F%28pi%29 then multiply left&right by LCD of 9,
h%5E2%2B6h=%289%2A68%29%2F%28pi%29
h%5E2%2B6h-612%2F%28pi%29=0
Use general solution to quadratic formula from there to find h. One value will make sense and the other will not.
About highlight%2811.25%29 meters


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"c" = -194 approximately.
h=%28-6%2Bsqrt%286%2A6-4%2A1%2A%28-194%29%29%29%2F%282%29