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

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) (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 =
:
diameter = 2r
:
It states,"diameter is always three times its height"; therefore
2r = 3h
r = h
Substitute h for r in the vol formula
= 1030
:
= 1030
:
= 1030
cancel the 3 into the 9
= 1030
Multiply both sides by 4
= 4120
divide both side by 3pi
=
:
= 437.145577
h = ; find the cube root of 437.145577
h = 7.59 feet is the height
;
;
Check solution by finding the volume;
find r
r = *7.59
r = 11.38
V =
V = 1029.33 ~ 1130

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