Blogging On Differentiation rule
We need to read the question and find a formula, or even probably two relate to the information that question told us. We need to know everything that might relate to the question, and solve the problem.
Exp: Water is flowing into a cone-shaped tank at the rate of 5 cubic inches per second. If the cone has an attitude of 4 inches and a base radius of 3 inches, how fast is the water level rising when the water is 2 inches deep?
The problem is given us the rate of change volume, dv/dt =5, r = 3, and asked to determine the rate change of height when h is 2, dh/dt when h=2.
We know the formula for conical volume is: V = 1/3 pai (r)^2 h
By similar triangle we have r/3=h/4,
So, r=3/4 h
V=1/3 pai r^2 h
V=1/3 pai (3/4h)^2 h
V= 1/3 pai 9/16 h^2 h
V= 3/16 pai h^3
dv/dt = 3/16*pai* 3h^2 (dh/dt)
5 = 3/16 pai 3(2)^2 (dh/dt)
20/9pai = dh/dt
The water level is rising at a rate of 20/9pai inches per second when the water is 2 inches deep.