A feeding trough full of water is 5 ft long and its ends are isosceles triangles having a base and height of 3 ft. Water leaks out of the tank at a rate of 5 (ft)^3/min. How fast is the water level falling when the water in the tank is 6 in. deep?
1 Answer
Jun 30, 2016
falling at a rate of 2ft /min
Explanation:
If you consider the generalised position when the depth of the water in the trough is at x where #x = x(t). Due to the similar triangles, the "width" of the water channel will also be x, as indicated in the drawing
We can say that the volume in the tank at that time,
so
taking the derivative wrt time
so
we know that
so so
so it's falling at a rate of 2ft /min at that moment