Question

Oil is poured on a flat surface and it spreads out forming a circle. the area of this circle is increasing at a constant rate of 10⁡cm2/s. determine the rate of change of the radius of the circle when the radius is 10⁡cm

Answer 1

Yay


derivitives

everything is taken derivitve in repsect to time

da/dt=10cm^2/s

alright
area=pir^2
da/dt=2pir dr/dt
10cm^2/s=2pir dr/dt
r=10
$\frac{10cm^2}{sec}=2\pi 10cm\frac{dr}{dt}$
$\frac{10cm^2}{sec}=20\pi cm \frac{dr}{dt}$
divide both sides by 20pi
$\frac{10cm^2}{20cm \pi sec}= \frac{dr}{dt}$
$\frac{1cm}{2\pi sec}= \frac{dr}{dt}$

the rate of change of the radius when radius=10 is $\frac{1cm}{2\pi sec}$