Mathematics - Application of Derivative Question with Solution | TestHub

Let $\theta$ be the semi-vertical angle and $r$ be the radius of the cone at time $t$. the radius of the cone at time $t$. Then, $r=20\tan \theta$$\Rightarrow \frac{dr}{dt}=20{\sec }^2\theta \frac{d\theta }{dt}$ $\Rightarrow \frac{dr}{dt}=20{\sec }^{2}30^{\circ }\times 2$ $[\because \theta =30^{\circ }$ and $\frac{d\theta }{dt}=2]$ $\Rightarrow \frac{dr}{dt}=20\times \frac{4}{3}\times 2\mathrm{cm}/\mathrm{s}=\frac{160}{3}\mathrm{cm}/\mathrm{s}$