Example 3-6-5 - Maple Help
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Chapter 3: Applications of Differentiation

Section 3.6: Related Rates

Example 3.6.5

A right-circular conical tank, whose cross-section through its axis is shown in Figure 3.6.4, is being filled with water at the constant rate λ.


At time t&Hat;, find h&period;t&Hat;, the rate of change of the height of the water, where t&Hat; is the moment when the volume is k times the volume of the tank, 0<k1.


The dimensions of the tank and the rate of fill are all in consistent units. The height of the tank is H, while the radius of the opening is R. The varying radius of the circle at the level of the water is rt (green dotted line in Figure 3.6.5(a)), and the varying height of the water is ht.


Hint: The volume of the tank is &pi;3 R2H

plots:-display(p||(1..5),scaling=constrained, axes=none);


Figure 3.6.5(a)   Conical tank

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