Answer:
When the radius is 11 feet, the area is changing at approximately 276.571 square feet per minute.
Step-by-step explanation:
We are given the following in the question:
[tex]\dfrac{dr}{dt} = 4\text{ feet per minute}[/tex]
Instant radius = 11 feet
Area of circle =
[tex]A = \pi r^2[/tex]
where r is the radius of the circle.
Rate of change of area of circle =
[tex]\dfrac{dA}{dt} = \dfrac{d}{dt}(\pi r^2) = 2\pi r\dfrac{dr}{dt}[/tex]
Putting all the values, we get,
[tex]\dfrac{dA}{dt} = = 2\pi (11)(4) = 88\pi = 276.571\text{ square feet per minute}[/tex]
Thus, when the radius is 11 feet, the area is changing at approximately 276.571 square feet per minute.
