# 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?

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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