Question

A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/sec. Find the rate at which its area is increasing when radius is 3.2 cm.

Answer 1

$$\begin{gathered} \text{Let}\mathit{\text{r}}\text{be the radius and}\mathit{\text{A}}\text{be the area of the circular disc at any time}\mathit{\text{t.}}\text{Then,} \\ \mathit{\text{A}}\text{=π}{\mathit{\text{r}}}^2 \\ \text{⇒}\frac{dA}{dt}\text{=2π}\mathit{\text{r}}\frac{dr}{dt} \\ \text{⇒}\frac{dA}{dt}\text{=2π×3.2×0.05}\left[\because r=3.2\mathrm{cm}\mathrm{and}\frac{dr}{dt}=0.05\mathrm{cm}/\sec \right] \\ \text{⇒}\frac{dA}{dt}{\text{=0.32π cm}}^2\text{/sec} \end{gathered}$$