Let
be the radius of the circle at the top of the water and
be the height of the water.
Then, using the picture in part (a) with a property of similar triangles gives the ratio between
and
as
On the other hand, by the volume formula for a cone, the volume
of water can be written as
Therefore, by differentiating with respect to
on both sides, we obtain
Since the volume changes at a rate of
, the rate of change of the height of the water when the height is
is