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Example 1:

The point of a fountain pen is placed on an ink blotter, forming a circle of ink whose area increases at the constant rate of 0.03 in.2/sec. Find the rate at which the radius of the circle is changing when the circle has a radius of ½ inch. We solve the problem in four steps.

 

Step 1

Label all quantities involved and draw a diagram.

t = time
A = area
r = radius of circle

Both A and r are functions of t. The diagram is shown in Figure 3.2.1.

03_continuous_functions-13.gif

Figure 3.2.1

Step 2

Write the given information in the form of equations.

dA/dt = 0.03, A = πr2.

The problem is to find dr/dt when r = ½.

Step 3

Differentiate both sides of the equation A = πr2 with respect to t.

03_continuous_functions-18.gif , whence 03_continuous_functions-19.gif

Step 4

Set r = ½ and solve for dr/dt.

03_continuous_functions-20.gif , so03_continuous_functions-21.gif

 
Home Continuous Functions Related Rates Examples Example 1:

Last Update: 2006-11-15