MathProblem 18 Sideways tank of gas problem

The gas tank of a truck is cylindrical in shape with a radius of r inches and a lengh of l inches, and tank lays on its side. With a measuring stick you note how many inches of gas are in the tank. Given this depth of gas, how many cubic inches of gas are in the tank? You may assume the tank is less than half full.

Solution

很基础的高中数学题。将圆柱体平放，里面装有gas，已知深度 \(d\)，求体积。这里就不求解了，高中的知识。

\[V=l\cdot([r^2\arccos{\frac{r-d}{r}}]-(r-d)\sqrt{2rd-d^2}) \]