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) $11\pi$

Option B is correct

If $A$ is the area of the circle corresponding to radius $r$, then $A = \pi {r^2}$ …(i)

Differentiating (i) w.r.t. $r$, we get $\cfrac{{dA}}{{dr}} = 2\pi r$

Therefore, ${\left( {\cfrac{{dA}}{{dr}}} \right)_{r = 6{\rm{cm}}}} = 2\pi \left( {6{\rm{cm}}} \right) = 12\pi {\rm{cm}}$