The area of a circle of radius r is given by and its circumference is given by C = 2πr. At a certain point in time, the radius of the circle is r = 8 inches and the area of the circle is changing at a rate of inches per second. How fast is the radius of the circle changing at this time?

the radius of the circle is changing at that time.

Step-by-step explanation:

Given:

Area of Circle

Radius

We need to find the radius of the circle changing at this time .

Solution:

To find the rate at which the radius of the circle is changing with respect to time we will apply derivative on Area of the circle.

Now we know that;

Applying derivative we get;

Now substituting the given value we get;

Hence the radius of the circle is changing at that time.