The radius of a sphere is increasing at the rate of 0.5 cm/minute. Th…

Surface area = $4 \pi r^2 = S$

$\Rightarrow \frac{d s}{d t}=8 \pi r \frac{d r}{d t}$

$\frac{dr}{dt} = 0.5 \frac{cm}{min}$

so  at r = 20

$\frac{ds}{dt} = 8 \pi × 20 × 0.5 = 80 \pi cm^2/min$