Suppose you are working for a manufacturing company that is

avissidep

avissidep

Answered question

2021-10-05

Suppose you are working for a manufacturing company that is analyzing a newer product using the following:
A=πr2
dAdt=2πr{(drdt}) Explain what the product engineers may be examining/testing/analyzing. Why is the factor {dr}{dt} needed?

Answer & Explanation

Bentley Leach

Bentley Leach

Skilled2021-10-06Added 109 answers

Step 1
We know that a circle of radius r, the area is πr2
Hence A=πr2 is pretty straightforward. It tells us that the engineers are analysing a product that has a circular part that changes in size while retaining the circular shape. We can also understand that area A is a function of the radius r.
Step 2
Now, differentiating A with respect to time t, gives us dAdt=πdr2drdrdt=2πrdrdt
This gives us the rate of change of area w.r.t time. We can see that it is dependent on the current radius r as well as the rate of change of radius w.r.t. time, i.e. drdt
It appears that the engineers are testing the rate of change of area using the radius and the rate of change of radius.

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