water flows from at 27 cubic centimeter per second, into a rectangular container of length 60cm, breadth 30cm and height 40 cm. if a 6:00pm the container was half full will be the height of water is at 6:04 pm?
volume = 60*30 * 40 = 72*10^3 cc
half volume = 36*10^3 cc when depth z = 20
surface area = 60*30 = 1.8*10^3 cm^2
so
rate of change of depth = volume rate / surface area
= 27 cc/s /1.8*10^3cm^2 ) = 15*10^-3 cm/s
go for 4*60 = 240 seconds = 2.4*10^2 s
change in depth = 1.5*10^-2 * 2.4*10^2 = 3.6 cm
so height is 20 + 3.6 = 23.6 cm