Question

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

• A. $\frac{l}{r}$
• B. $\frac{l}{r^{2}}$
• C. r
• D. $r^{2}$

Answer 1

Answer: (C)

r

Answer 2

$\because$ Surface area $s = 4\pi r^{2}$ and $\frac{dr}{dt} = 2$

$\therefore$ $\frac{ds}{dt} = 4\pi \times 2r\frac{dr}{dt} = 8\pi r \times 2 = 16\pi r$ ⇒ $\frac{ds}{dt} \propto r$.