SOLUTION: Hi. May I have some help with the following equation? Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How

Algebra ->  Equations -> SOLUTION: Hi. May I have some help with the following equation? Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How       Log On


   

Question 121384: Hi. May I have some help with the following equation?
Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile (to the nearest hundredth of a foot) when it contains 900 ft3 of grain?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Grain is falling from a chute onto the ground, formi9x^2ng a conical pile whose diameter is always three times its height. How high is the pile (to the nearest hundredth of a foot) when it contains 900 ft3 of grain?
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Let the height be "x" ft. ; The diameter is "3x" : radius = (3x/2)
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Volume = (pi)r^2 h
900 = (pi)(3x/2)^2*x
900 = (pi)(9x^2/4)x
900/(pi) = (9/4)x^3
(4/9)(900/pi)= x^3
400/pi = x^3
x = 5.0308 ft (height)
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Cheers,
Stan H.