The radius of a circle is increasing at a constant rate of 0.2 meters per second. what is the rate increase in the area of the circle at the instant when the circumference of the circle is 20π meters? v

The rate of increase in the area of the circle at the instant when the circumference of the circle is 20π m is 12.56 .

Given :

Radius of a circle is increasing at a constant rate of 0.2 m/sec.

Circumference of the circle at an instant is m.

Solution :

We know that area of the circle is,

--- (1)

Now differentiate equation (1) with respect to time t,

Given that

so,

  ------ (2)

We also know that circumference of the circle is,

--- (3)

At from equation (3) we get,

Now put the value r in equation (2) we get

The rate of increase in the area of the circle at the instant when the circumference of the circle is 20π m is 12.56 .

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This question involves the concepts of circumference, area, and derivative.

The rate of increase in area is "12.57 m²/s".

The area of a circle is given as:

Taking the derivative with respect to time (t) on both sides, we get:

where,

= rate of change in area = ?

= Circumference of the circle = 20π m

= rate of increase in radius = 0.2 m/s

Therefore,

Learn more about the area of the circle here:

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The attached picture shows the area of circle.

u=13

v=30

s/t=u+1\2at

=13+431/2

=13+265.5

=278.5