i want to find V(t)(adsbygoogle = window.adsbygoogle || []).push({});

At first i found this problem was very simple but when i try to write differential equations i ended up with these

V' = kA thats for sure

then i confined the problem only to spherical shape and no other shapes of raindrops involved

as i cant express A in term of V alone( surface area of sphere = 4∏r^{2}, volume of sphere is 4/3∏r^{3}) then i have to

use chain rule, dV/dt= dV_{dr}dr_{dt}substitute dV/dt from

V'=k4∏r^{2}

i get

4∏r^{2}r'= K4∏r^{2}

r'=k

r = kt+c

r^{3}= (kt+c)^{3}

4∏r^{3}/3 = (kt+c)^{3}4∏/r=V(t)

im i correct? the answer to this problem is V'=kV^{2/3}im not sure how they transform Area to variable V alone

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# A spherical raindrops evaporates at rate proportional to surface area?

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