A) A cylindrical tank with radius 8 m is being filled with water at a rate of 2 m3/min. How fast is the height of the water increasing (in m/min)?

Let r represent the radius of the cylindrical tank in m, let h represent the height of the water in the tank in m,
and let v represent the volume of the water in the tank in m. Writing an equation for V in terms of r and h
gives the following result.

b) We are given that the radius of the tank is 8 and therefore the radius of the column of water that is being
measured remains at a constant 8 m. Substituting the value r = 8 into the volume equation gives a simplified
equation for V in terms of h, as follows.
V=