Answer:
163.4 or [tex]52\pi[/tex] m2/s
Explanation:
The rate of change of the radius is 1 m/s
[tex]\dfrac{dr}{dt}=1[/tex]
The area of a circle is
[tex]A=\pi r^2[/tex]
We differentiate this to get the rate of change of the area with the radius:
[tex]\dfrac{dA}{dr}=2\pi r[/tex]
The rate of change of the area is
[tex]\dfrac{dA}{dt} = \dfrac{dA}{dr}\times\dfrac{dr}{dt}=2\pi r \times1 = 2\pi r[/tex]
At r = 26 m,
[tex]\dfrac{dA}{dt}=2\pi \times26=52\pi=163.4[/tex]
