help with this problem please...a spherical raindrop evaporates at a rate proportional to its surfacce area. write a differential equation for the volume of the raindrop as a function of time?
2006-09-24 08:16:11 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
can u explain how to get the first answer?
2006-09-24 10:33:45 · update #1
i can't figure out where v^2/3 comes from
2006-09-24 10:39:06 · update #2
dV/dt=kV^(2/3), where k is an arbitrary constant of proportionality.
2006-09-24 08:20:02 · answer #1 · answered by Pascal 7 · 0⤊ 0⤋
let v be the volume, r be radius,
v=4/3 * PI *r squared..
r=square root of [(3*v)/(4*pi)]
let s be surface are=4*PI*r squared
s=4*PI*3*v/(4*PI) from volume
dv/dt=dv/dr * dr/ds
find differencials and substitute to get answer
2006-09-24 15:21:55 · answer #2 · answered by ashwin_hariharan 3 · 1⤊ 0⤋