Mathematics - Application of Derivative Question with Solution | TestHub

Let $A$ sq. units in the area measure when the radius is $r$ units. their $A=\pi r^2$ Differentiate both side w.r.t ' $t$ ' $\frac{dA}{dt}=2\pi r\frac{dr}{dt}$ ...(i)) We have, $\frac{dA}{dt}=3c\frac{dr}{dt}$ From eqn (i), we get $3c\cdot \frac{dr}{dt}=2\pi r\cdot \frac{dr}{dt}\Rightarrow 3c=2\pi r$ Now, $c=\frac{2}{3}\pi (6)=4\pi$ when $r=6$