Question

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is

(a) $10\pi$

(b) $12\pi$

c) $8\pi$

d) $11\pi$

Answer 1

If A is the area of the circle corresponding to radius r, then $A=\pi r^2$
On differentiating w.r.t t, we get
$\frac{dA}{dr}=2\pi r$
On putting $r=6,weget\left(\frac{dA}{dr}\right)=2\pi \left(6\right)=12\pi c{m}^2/cm$
Hence, the required rate of change of the area of a circle is $12\pi c{m}^2$ per cm.
Hence, the correct options is (b).