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For a circle with radius 20 units, the rate of change of radius is 3 unit/time, then what is the rate of change of area?
1. 60π 
2. 80π 
3. 100π 
4. 120π 

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Correct Answer - Option 4 : 120π 

Concept:

The rate of change of the value of a function f(x) with respect to a variable t, is given by: \(\rm \frac {df(x)}{dt}\)

The area of any circle is π rwhere r is the radius of the circle.

 

Calculation:

We know, area of any circle,

A = π r2

Differentiating the equation we get,

⇒ \(\rm dA \over dt\)= 2π r × \(\rm dr \over dt\)

Given, r = 20, \(\rm dr \over dt\)= 20

Putting the values we get,

⇒ \(\rm dA \over dt\) = 2 π × 20 × 3

⇒ \(\rm dA \over dt\) = 120 π 

So, the right answer is 120π 

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