







Related rates 
20140130 

Veronica pose la question : A container is the shape of an inverted right circular cone has a radius of 1.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 1.00 inches deep, the surface level is falling at the rate of 2.00 inches/second. Find the rate at which the water is being drained. Penny Nom lui répond. 





Water pouring into a conical tank 
20111121 

Patience pose la question : Hi my name is patience and I'm having a problem with this question.
Water pours into a conical tank of semi vertical angle 30 degrees at the rate of 4 cm^3/s, where h is the depth of the water at time t. At what rate is the water rising in the tank when h = 10 cm?
Thank you Penny Nom lui répond. 





Two conical tanks 
20110217 

rustom pose la question : Two vertical conical tanks (both inverted) have their vertices connected by a short horizontal pipe.
One tank, initially full of water, has an altitude of 6 ft. and a diameter of base 7 ft.
The other tank, initially empty, has an altitude of 9 ft., and a diameter of base 8 ft.
If the water is allowed to flow through the connecting pipe, find the level to which
the water will ultimately rise in the empty tank (Neglect the water in the pipe.) Penny Nom lui répond. 





Calibrating a conical tank 
20110205 

Bill pose la question : Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Stephen La Rocque and Penny Nom lui répond. 





Water drains from a conical tank 
20090311 

Tyler pose la question : Water drains from a conical tank at the rate of 5ft/min^3. If the initial radius of the tank is 4' and the initial height is 10'.
a) What is the relation between the variables h and r? (height and radius)
b) How fast is the water level dropping when h=6'?
Thanks for the help, i'm stumped. Penny Nom lui répond. 





Water in a conical tank 
20070910 

Greg pose la question : Joe is conducting an experiment to study the rate of flow of water from a conical tank.
The dimensions of the conical tank are:
Radius at the initial water level = 13.7 cm
Radius at the reference point = 12.8 cm
Initially the tank is full of water. There is a circular orifice at the bottom of the conical
tank with a diameter of 0.635 cm. The water drains from the conical tank into an empty
cylindrical tank lying on its side with a radius of 0.500 ft and a length L (ft).
Joe observed the water discharged with an average velocity of 1.50 m/s as the water level
lowered from the initial height of 14.0 cm to 5.00 cm in the conical tank. Answer the
following:
1. If the initial height of water in the conical tank is 14.0 cm (measured from the
reference point, see Fig. 1), how long in seconds will it take for the water level to drain to
a height of 5.00 cm?? NOTE: Height refers to the vertical height.
What formula would I use to find out how long in seconds it takes for the water level to drop? Harley Weston lui répond. 

