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=dVdt where V is the volume and dV/dt is the volume flow (time) rates and
v=dhdt=dxdt=dydt=dsdt where h, x, y, s are distances and v is velocity.
Thus, the formula Q = vA can be written as
dVdt=dhdtA
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 Ay, 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
Ay=a+by+cy2+dy3
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,
Ay=a+by+cy2
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.