Answer:
The rate of change is of of the area when the radius is 4 centimeters [tex]48\pi[/tex] square centimeters.
Step-by-step explanation:
Area of a circle:
The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
Implicit derivative:
To solve this question, we have to derivate implictly the equation as a function of t. Thus:
[tex]\frac{dA}{dt} = 2\pi r \frac{dr}{dt}[/tex]
The radius of a circle is increasing at a rate of 6 centimeters per minute.
This means that [tex]\frac{dr}{dt} = 6[/tex]
Find the rate of change of the area when the radius is 4 centimeters.
This is [tex]\frac{dA}{dt}[/tex] when [tex]r = 4[/tex]. Thus
[tex]\frac{dA}{dt} = 2\pi r \frac{dr}{dt} = 2\pi(4)(6) = 48\pi[/tex]
The rate of change is of of the area when the radius is 4 centimeters [tex]48\pi[/tex] square centimeters.
