# Thread: Related rates, Differential equations calculus.

1. ## Related rates, Differential equations calculus.

Once a spherical shaped soufflé is put in the oven, its volume increases at a rate proportional to its radius.
1. Show that the radius r cm of the soufflé, at t minutes after it has been put in the oven, satifies the differential equation dr/dt = k/r , where k is a constant.

2. Given that the radius of the soufflé is 8 cm when it goes in the oven, and 12 cm when it´s cooked 3 minutes later, find, to the nearest cm, its radius after 15 minutes in the oven.
Thanks!

2. Grrr.... Scribbled it down and scanned it, hopefully you can read it.

3. Thank you for your quick response, but I wasn´t able to open the file.

4. I am getting a slightly different answer.

$\displaystyle \frac{dr}{dt}=\frac{k}{r}$

Separate variables:

$\displaystyle rdr=kdt$

Integrate:

$\displaystyle \int{r}dr=\int{k}dt$

$\displaystyle \frac{r^{2}}{2}=kt+c$

Using r(0)=8:

$\displaystyle 32=k(0)+c$

c=32

Using t(3)=12:

$\displaystyle 72=k(3)+32$

$\displaystyle k=\frac{40}{3}$

$\displaystyle r=\sqrt{2(kt+32)}$

At t(15):

$\displaystyle r=\sqrt{2(\frac{40}{3}(15)+32)}=4\sqrt{29}\approx{ 21.54}$