# Related rates, Differential equations calculus.

• May 21st 2008, 04:33 AM
pantera
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!
• May 21st 2008, 05:02 AM
iphysics
Grrr.... Scribbled it down and scanned it, hopefully you can read it.

http://img372.imageshack.us/img372/2443/eqgd7.png
• May 21st 2008, 07:47 AM
pantera
Thank you for your quick response, but I wasn´t able to open the file.
• May 21st 2008, 11:07 AM
galactus
I am getting a slightly different answer.

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

Separate variables:

$rdr=kdt$

Integrate:

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

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

Using r(0)=8:

$32=k(0)+c$

c=32

Using t(3)=12:

$72=k(3)+32$

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

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

At t(15):

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