Answer:
.
Step-by-step explanation:
Let x represent height of the cone.
We have been given that Sand pouring from a chute forms a conical pile whose height is always equal to the diameter.
We know that radius is half the diameter, so radius of cone would be .
We will use volume of cone formula to solve our given problem.
Upon substituting the value of height and radius in terms of x, we will get:
Now, we will take the derivative of volume with respect to time as:
Upon substituting and , we will get:
Therefore, the sand is pouring from the chute at a rate of .