**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.

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