Answer:
2 meter square per minute
Step-by-step explanation:
Given the circumference is of the circle is increasing at a rate of 0.5 m/minute
We know that C = 2πr
We know that the area of the circle(A) = π[tex]r^2[/tex]
Let π=a
[tex]r=\frac{C}{2a}[/tex]
A = a [tex](\frac{C}{2a})^2[/tex]
[tex]A=\frac{C^2}{4a}[/tex]
Differentiate both sides with respect to time
[tex]\frac{dA}{dt}=\frac{C}{2a}\frac{dC}{dt}[/tex]
C at r= 4 is C = 8a
Given [tex]\frac{dC}{dt}[/tex] = 0.5
[tex]\frac{dA}{dt}=\frac{8a}{4a}[/tex] = 2
