Sand pouring from a chute forms a conical pile whose height is always equal to the diameter. If the height increases at a constant rate of 5 ft/min, at what rate is sand pouring from the chute when the pile is 10 ft high?

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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 .

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step-by-step explanation: