Understand why this calculator technique works
In Hydraulics, discharge or volume flow rate is given by the formula
$Q = vA$
Where
$Q$ = the discharge or volume flow rate
$v$ = velocity of flow
$A$ = cross-sectional area of flow
The equivalent of the above elements in Calculus are:
$Q = \dfrac{dV}{dt}$ where V is the volume and dV/dt is the volume flow (time) rates and
$v = \dfrac{dh}{dt} = \dfrac{dx}{dt} = \dfrac{dy}{dt} = \dfrac{ds}{dt}$ where h, x, y, s are distances and v is velocity.
Thus, the formula Q = vA can be written as
$\dfrac{dV}{dt} = \dfrac{dh}{dt}A$
which is the formula we are going to use in our calculator.
For the area A
The general prismatoid is a solid in which the area of any section, say A_{y}, parallel to and at a distance y from a fixed plane can be expressed as a polynomial in y not higher than third degree, or
$A_y = a + by + cy^2 + dy^3$
Common solids like cone, prism, cylinder, frustums, pyramid, and sphere are actually prismatoids in which any area parallel to a base is at most a quadratic function in height y. Thus,
$A_y = a + by + cy^2$
We can therefore use the Quadratic Regression in STAT mode of the calculator to find the area in relation with its distance from a predefined plane.