A Difficult Problem?

Many people land on this page of my other blog in search of an answer for this problem:

A circular lake 1.0 km in diameter is 10 m deep. Solar energy is incident on the lake at an average rate of 200 W/m². If the lake absorbs all this energy and does not exchange heat with its surroundings, how long will it take to warm from 10°C  to 20°C ?

as seen in the following snapshot:


Now, I do offer a pathway to the solution there but I feel that not providing the final answer is tantamount to cheating on my part. So, this being a ‘Physics blog’, I provide the entire solution here (I don’t know or care what good does it do to those ‘searchers’!):

t=\frac{Q}{S.A}=\frac{m.C.\Delta T}{S.A}=\frac{(\rho .V)C.\Delta T}{S.A}=\frac{\rho(A.h)C.\Delta T}{S.A}=\frac{\rho .h.C.\Delta T}{S}

\Rightarrow t=\frac{1000\times 10\times 4200\times (20-10)}{200}= 2.1\times 10^6s=24d~7h~20m.

Any Thoughts?

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