Understand why this calculator technique works
In Hydraulics, discharge or volume flow rate is given by the formula
= the discharge or volume flow rate
= velocity of flow
= cross-sectional area of flow
The equivalent of the above elements in Calculus are:
where V is the volume and dV/dt is the volume flow (time) rates and
where h, x, y, s are distances and v is velocity.
Thus, the formula Q = vA can be written as
which is the formula we are going to use in our calculator.
For the area A
The 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
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,
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.