Need help solving this trapezoidal problem

[Trey Chandler]

Homework Statement:

Shown below is a cylindrically shaped fuel tank of diameter D and length L, filled to a variable depth h. The volume of the fuel is calculated by measuring the depth (h) of the fuel in the tank in inches. Perform this calculation using the Trapezoid Method. Plug in the values given to you (in a separate file) to find the volume, measured in gallons.

My values are D = 12(ft), L = 20(ft), h = 91(in)

Relevant Equations:

x^2 + y^2 = r2

This is my attempt at the problem I'm pretty sure the answer is supposed to be in gallons but I don't know what I'm doing clearly.

 

[Mark44]

It looks like your answer is in units of cubic inches. One gallon = 231 cu. inches.

 

[haruspex]

I am not able to follow your calculation. E.g. I see the equation $y=\sqrt{36-x^2}+h$ but cannot see what definition of x and y would make that correct.
Please define x and y, and develop your equations purely algebraically. Avoid plugging in numbers until the final step.

 

[archaic]

Your height function is wrong I think. Here's a clearer drawing of your situation.

Do you think that you're always adding that increment to the semi circle height function? What about near the its endpoints where it becomes curved?