Question

need help plz :)
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A spherical raindrop evaporates at a rate proportial to its surface area . write a differential equation for the volume of the rain drop as a function of time.

Answer 1

First find Volume as a function of time & then make a differential equation by eliminating the arbitrary constant(s)..

Answer 2

how could i do that ?

Answer 3

"A spherical raindrop evaporates at a rate proportial to its surface area"
Can you write the corresponding equation for this ^^ statement ??

Answer 4

no

Answer 5

Can you tell me the formula for surface area for a sphere ?
Please don't let me down :P

Answer 6

\(\Huge S=4\pi r^2\)

Answer 7

O.O
So biggggg..
LOL

Answer 8

BTW, rate of evaporation can be considered as dV/dt (or -dV/dt ; I prefer working with positive, the constant of proportionality can be considered negative).

Hence, the sentence
"A spherical raindrop evaporates at a rate proportial to its surface area"
is equivalent to
\[\frac{ dV }{ dt }=kr^2\]
where k is a constant.

Answer 9

We already have r as a function of V.
k is the only arbitrary constant here..eliminate k to get the final answer..

Answer 10

plz continue

Answer 11

EOL :P

Answer 12

plzzzz

Answer 13

do it or ill tag mashy

Answer 14

V = volume, t = time, and S = surface area. Then dV
dt =
−kS, for k > 0.

Answer 15

it will help u

Answer 16

https://www.math.ucdavis.edu/~hunter/m22b/HWsol12.pdf

Answer 17

\(dv=-ks dt\)?!
ot
\(dv=-kr^2 dt\)

Answer 18

ok thx both of you !
@LastDayWork @HARSH123 !