Answer:
[tex]\frac{dA}{dt} = 188.5 m^2/s[/tex]
Explanation:
As we know that area of the circle at any instant of time is given as
[tex]A = \pi r^2[/tex]
now in order to find the rate of change in area we will have
[tex]\frac{dA}{dt} = 2\pi r\frac{dr}{dt}[/tex]
here we know that
rate of change of radius is given as
[tex]\frac{dr}{dt}= 1 m/s[/tex]
radius of the circle is given as
[tex]r = 30 m[/tex]
now we have
[tex]\frac{dA}{dt} = 2\pi (30)(1)[/tex]
[tex]\frac{dA}{dt} = 60\pi[/tex]
[tex]\frac{dA}{dt} = 188.5 m^2/s[/tex]
