Now we plug in for , which gives us
Now we would have to use a lot of algebra to simplify this but, fortunately, we can just plug in
(0, ) for x and y and solve from there.
- Water is draining at the rate of 48π ft^3 /sec from the vertex at the bottom of a conical tank whose
diameter at its base is 40 feet and whose height is 60 feet.
(a) Find an expression for the volume of water (in ft^3 /sec) in the tank, in terms of its radius, at
the surface of the water.
The formula for the volume of a cone is V = πR^2 H, where R is the radius of the cone and H
is the height. The ratio of the height of a cone to its radius is constant at any point on the edge of
the cone, so we also know that = = 3. (Remember that the radius is half the diameter.) If
we solve this for H and substitute, we get
H = 3R
V = πR^2 (3R) = πR^3
