SOLUTION: Hi I'm having a hard time figuring out the answer to this problem: Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times it

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Question 196642: Hi
I'm having a hard time figuring out the answer to this problem:
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 1030 ft^3 of grain?
Thanks!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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 1030 ft^3 of grain?
:
The volume of a cone: V = %281%2F3%29pi%2Ar%5E2%2Ah
:
diameter = 2r
:
It states,"diameter is always three times its height"; therefore
2r = 3h
r = 3%2F2h
Substitute 3%2F2h for r in the vol formula
%281%2F3%29pi%2A%28%283%2F2%29h%29%5E2%2Ah = 1030
:
%281%2F3%29pi%2A%289%2F4%29h%5E2%2Ah = 1030
:
%281%2F3%29pi%2A%289%2F4%29h%5E3 = 1030
cancel the 3 into the 9
pi%2A%283%2F4%29h%5E3 = 1030
Multiply both sides by 4
pi%2A3%2Ah%5E3 = 4120
divide both side by 3pi
h%5E3 = 4120%2F%283pi%29
:
h%5E3 = 437.145577
h = 437.145577%5E%281%2F3%29; find the cube root of 437.145577
h = 7.59 feet is the height
;
;
Check solution by finding the volume;
find r
r = 3%2F2*7.59
r = 11.38
V = %281%2F3%29pi%2A11.38%5E2%2A7.59
V = 1029.33 ~ 1130