Find the rate of change of the area of a circle with respect to its radius $r$ when $r = 3$ cm.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $6π\,cm^2/cm$
Let A be the area of a circle of radius $r$, then $A = πr^2$.
∴ The rate of change of area A with respect to its radius $r$
$=\frac{dA}{dr}=π.2r= 2πг$.
When $r = 3$ cm, $\frac{dA}{dr}=2π × 3 = 6π$.
Hence, the area of the circle is changing at the rate of $6π\,cm^2/cm$.