The axis of a storage tank in the form of a right circular cylinder is horizontal (see figure). The radius and length of the tank are 1 meter and 3 meters, respectively.

(a) Determine the volume of fluid in the tank as a function of its depth d.

(b) Use a graphing utility to graph the function in part (a).

(c) Design a dip stick for the tank with markings of 1/4, 1/2, 3/4. 

(d) Fluid is entering the tank at a rate 1/4 of cubic meter per minute. Determine the rate of change of the depth of the fluid as a function of its depth d.

(e) Use a graphing utility to graph the function in part (d).
When will the rate of change of the depth be minimum?
Does this agree with your intuition? Explain.

Transcribed Image Text:

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