Answer with Step-by-step explanation:
We are given that
[tex]\frac{dA}{dt}=150m^2/s[/tex]
a.Radius =25 m
We have to find rate of change of radius.
We know that
Area of circle,[tex]A=\pi r^2[/tex]
Differentiate w.r.t time
[tex]\frac{dA}{dt}=2\pi r\frac{dr}{dt}[/tex]
Substitute the values then we get
[tex]150=2\pi (25)\frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt}=\frac{150}{50\pi}=\frac{3}{\pi} m/s[/tex]
[tex]\frac{dr}{dt}=\frac{3}{\pi} m/s[/tex]
b.A=[tex]1000m^2[/tex]
Substitute the values then we get
[tex]1000=\pi r^2[/tex]
[tex]\pi=3.14[/tex]
[tex]r^2=\frac{1000}{3.14}[/tex]
[tex]r=\sqrt{\frac{1000}{3.14}}=17.8m[/tex]
[tex]\frac{dA}{dr}=2\pi r\frac{dr}{dt}[/tex]
Substitute the values then we get
[tex]150=2\pi(17.8)\frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt}=\frac{150}{2\pi(17.8)}=\frac{150}{35.6\pi}[/tex]m/s
[tex]\frac{dr}{dt}=\frac{75}{17.8\pi}[/tex]m/s
