question_answer

The rate of change of the surface area of a sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to                                                                                  [Karnataka CET 2003]

A)            \[\frac{1}{r}\]

B)            \[\frac{1}{{{r}^{2}}}\]

C)            \[\because \]Surface area \[s=4\pi {{r}^{2}}\] and \[\frac{dr}{dt}=2\]                    \ \[\frac{ds}{dt}=4\pi \times 2r\frac{dr}{dt}\] = \[8\pi r\times 2=16\pi r\]Þ  \[\frac{ds}{dt}\propto r\].

D)            \[{{r}^{2}}\]