Question

What is the rate of change of the area of a circle with respect to the radius when the radius is r = 3in?

Answer 1

The rate of change of the area of a circle with respect to the radius is given by the derivative of the area function, which can be found using the power rule of differentiation.

Step-by-step explanation:

The rate of change of the area of a circle with respect to the radius is called the derivative of the area function. The area of a circle is given by the formula A = πr², where π is a mathematical constant approximately equal to 3.14159. To find the derivative, we can differentiate the area formula with respect to the radius.

Using the power rule of differentiation, which states that the derivative of
`x^n is n*x^(n-1)`, we can differentiate A = πr² as follows:

dA/dr = 2πr

So, when the radius is r = 3in, the rate of change of the area of the circle with respect to the radius is dA/dr = 2π(3in) = 6πin²/in.