The height of a grain of a cylindrical silo is is increasing at a constant rate of 4 feet per minute at what rate is the volume of grain in the cylinder if the radius of the silo is 10 feet?

The rate of change of the volume of the cylinder when the radius is 10 ft is

Step-by-step explanation:

This is a related rates problem. A related rates problem is a problem in which we know the rate of change of one of the quantities (the height of a grain) and want to find the rate of change of the other quantity (the volume of grain in the cylinder).

The volume of a cylinder is given by

V and h both vary with time so you can differentiate both sides with respect to time, t, to get

Now use the fact that and

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step-by-step explanation:

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