SOLUTION: Sand 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 hundreth of a foot) when

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Sand 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 hundreth of a foot) when       Log On


   

Question 1134669: Sand 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 hundreth of a foot) when it contains 1000 ft^3 of sand?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


V+=+%281%2F3%29%28pi%29%28r%5E2%29%28h%29

d = 3h, so r = (3/2)h

1000+=+%281%2F3%29%28pi%29%28%283%2F2%29h%29%5E2%28h%29
1000+=+%281%2F3%29%28pi%29%289%2F4%29%28h%5E3%29
h%5E3+=+4000%2F%283%28pi%29%29
h+=+%284000%2F%283%28pi%29%29%29%5E%281%2F3%29

Which to 5 decimal places is 7.51501, so rounding to the nearest hundredth is not a good choice. But since that's what it asks for....

ANSWER: 7.52 feet.