Answer:
Rate of area with respect to its radius is 10π cm²/cm.
Step-by-step explanation:
I assume the question is "At what rate in cm square per cm ...", as it asks for the area with respect to its radius.
Rate of change of Area respect to its radius = [tex]\boxed{\frac{dA}{dr} }[/tex]
[tex]Area\ (A)=\pi r^2[/tex]
[tex]\displaystyle \frac{dA}{dr} =\pi(2)r^{(2-1)}[/tex]
[tex]\bf \displaystyle \frac{dA}{dr} =2\pi r[/tex]
When the radius is 5 cm → substitute r with 5 cm
[tex]\displaystyle \frac{dA}{dr} (5)=2\pi (5)[/tex]
[tex]=10\pi\ cm^2/cm[/tex]
