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Question
Assume that a spherical rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop
Solution
Volume od sphere V = `4/3 pi"r"^3`
`"dV"/"dt" = 4 pi"r"^2 * "dr"/"dt"`
Surface area = `4 pi"r"^2`
Given, `"dV"/"dt" oo ("S"*"A")`
`"DV"/"dt" = - "k" ("S"*"A")` ........[k - constant]
`4pi"r"^2 * "dr"/"dt" = - "k"(4pi"r"^2)`
`"dr"/"dt" = - "k"`
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