Modified Fuel Tank Problem

Consider the fuel tank shown to the right having the dimensions:

A measuring stick is used to calculate the volume of fuel in the tank. Derive a formula which will calculate the volume of fuel in the tank (in gallons) as a function of the reading (in inches) on the measuring stick.

Provide a graph which depicts this mathematical relationship. The graph's independent variable (x axis) should be inches.

Show all mathematics. Provide a sample calculation to demonstrate your equation works.

Modified Fuel Tank Approved Solution

Some notes:

V₁ domain:

V₂ domain:

or

(full large tank volume)

Large Tank

Sector Area

Triangle Area

Large Tank

Fluid Area

Large Tank - Fluid Volume

Small Tank

(full small tank volume)

Sector Area

Triangle Area

Small Tank

Fluid Area

Small Tank - Fluid Volume

The volume of the full small tank is:

Creating some logic to add the discontinuous functions (since the small tank's volume is complex below D or above 2*R₁ - D) so both the large and small tank volume functions can be graphed together: