MA 16500 Lecture Notes - Lecture 17: Airco Dh.2
6 Jun 2018
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Ex: A tank is in the shape of an inverted right circular cone with height and radius .m4m2
Water is poured How fast is the height of water rising when m/min.2 3.h= 3
In this problem, we first see that we are trying to find the rate of change of the cone as it is
related to the height. As such, we’re going to put all of our constant in forms of h. In this case,
we see that the radius is half of height, and we’ll have that done accordingly
.5hr = 0
Next, we are going to have our formula for the volume of a cone
πr hV =3
12
Knowing that, in this case, the radius is half the height, we are going to plug that in accordingly,
and thus we are going to have
π( ) hV =3
1
2
h2
The next part is fairly simple, as all we have to do is to factor out r = 0.5h, and thus, our equation
is in forms of height
πV=3
1
4
h3
Now, since we need to know the rate of change of the height, we are going to different the
volume by relation of height and we are going to differentiate the height while keeping the rate
of change of the height in mind, and thus we’ll get
π(h)( )
dt
dh =4
12
dt
dh
