The rate of change of the area is ______ square meters per minute.

Question

The radius of a circle is decreasing at a rate of 2 meters per minute.

When the radius is 14 meters, then how fast is the area changing?

The rate of change of the area is ______ square meters per minute.

(Enter your answer as a decimal number rounded to 2 places.)

Answer 1

Answer 2

"the radius of a circle is decreasing at a rate of 2 meters per minute" means dr/dt = -2

You are being asked about the area rate of change and the equation that relates area and radius is:

A = πr²

Take the derivative with respect to time by using the power rule and the chain rule:

dA/dt = 2πr•(dr/dt)

Plug in dr/dt = -2 and r = 14 to get:

dA/dt = 2π(14)•(-2)

dA/dt = -56π m²/minute (you can convert this to a decimal and round it)