



 
Hi Greg, The stream of water flowing out of the tank is in the shape of a circular cylinder of radius 0.635/2 cm. The volume of a circular cylinder is given by V = π r^{2} h where in your case r = 0.635/2 cm and V and h are functions of time. Thus, differentiating both sides
and you know that h'(t) = 1.50 m/s so this allows you to calculate V'(t). Now notice that the rate at which the volume of water flowing out of the tank is the rate at which the volume of water on the conical tank is decreasing. Hence the amount of water in the conical tank is changing at the rate of V'(t) m/s. The volume of a cone is 1/3 π r^{2} h where r is the radius and h is the height. Again in your case r and h are functions of time. You didn't send us Fig. 1 but I expect there is enough information in the figure to find a relationship between r and h, probably using similar triangles. This will allow you to write the volume of water in the tank as a function of one variable, either r or h. which should then allow you to complete the problem. Harley  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 