Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of water remaining. The tank initially contains 275 liters and 25 liters leak out during the first day. a) When will the tank be half empty? t=daysb) How much water will remain in the tank after 5 days? V= L

a) 2.56 days b) Zero Liters

Step-by-step explanation

let initial volume of tank be V₀ and volume at time t be V.

Rate is proportional to square root of volume of remaining water, therefore;

 where K is the proportionality constant.

   integrating both sides gives

at day one, t = 1 ; V = 25 Liters. Therefore;

K = 17.548

a) when tank is half V = 275/2 = 137.5

t = 2.56 days

b) How much water will remain after 5 days

V = 275 liters

Remaining water = 275 - 275 = O

4.

step-by-step explanation:

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