1. Sand falling from a chute forms a conical pile whose altitude is always equal to 4/3 the radius of the base. (a) How fast is the volume increasing when the radius of the base is 3 ft and is increasing at a rate of 3 in/min

The volume is increasing at a rate of 16286 in³/min.

Step-by-step explanation:

a) The volume of a cone is given by:

Where:    

r: is the radius

h: is the height

The rate of change of the volume can be calculated by using the chain rule:

Since h = 4/3 r we have:

   (1)    

With:

= 3 in/min

And by entering the above values into equation (1) we have:

Therefore, the volume is increasing at a rate of 16286 in³/min.

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