Question

The radius of a circular plate is increasing at the rate of 0.01 cm/sec. The rate of increase of its area when the radius is 12 cm, is
(a) 144 π cm²/sec
(b) 2.4 π cm²/sec
(c) 0.24 π cm²/sec
(d) 0.024 π cm²/sec

Answer 1

(c) 0.24 π cm²/sec

$$\begin{gathered} \text{Let}\mathit{\text{r}}\text{be the radius and}\mathit{\text{A}}\text{be the area of the circular plate at any time}\mathit{\text{t.}}\text{Then,} \\ \mathit{\text{A}}\text{=}\mathrm{\pi }{r}^2 \\ \text{⇒}\frac{dA}{dt}\text{=2π}\mathit{\text{r}}\frac{dr}{dt} \\ \text{⇒}\frac{dA}{dt}\text{=2π}\left(12\right)\left(0.01\right) \\ \text{⇒}\frac{dA}{dt}{\text{=0.24π cm}}^2\text{/sec} \end{gathered}$$