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 1110 ft3 of grain?

Given that grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height.

So if D is the diameter and h is the height of the conical pile then we can write:

D=3h

We know that diameter = 2r, where r is the radius

2r=3h

Volume of conical pile is given by formula

Given that volume is 1110 cubic feet.

Now plug the values of Volume and r into equation of volume

take cube root of both sides

7.78103342467=h

Hence height is approx 7.78 feet.

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step-by-step explanation: