[Guest]

A real life example of calculus in action:

A barrel of oil is lying on its side. It has one of its ends firmly attached to the wall (Meaning the barrel cannot be repositioned.) A dipstick can be used from the top of the rounded side to determine the height of the oil remaining in the barrel. Write a function to get the volume of the oil from the height of the oil on the dipstick. The barrel has a 22" diameter (11" radius) and a length of 33."

[bonanova]

V_oil = 33{121[pi - cos^-1([h-11]/11)] + (h-11) sqrt(22h - h²)} in³

Special cases:

Empty [h=0]: V_oil

= 33{121[pi - cos^-1(-1)] + (-11) sqrt(0)} in³

= 33{121[pi - pi] + 0}

= 0 in³

Full [h=22]: V_oil

= 33{121[pi - cos^-1(+1)] + (11) sqrt(22₂ - 22²)} in³

= 33{121[pi - 0] + 0}

= 33pi x 11² in³

= 12544.38 in³

Half-full [h=11]: V_oil

= 33{121[pi - cos^-1(0)] + (0) sqrt(11²)} in³

= 33{121[pi - pi/2] + 0}

= 33pi/2 x 11² in³

= 6272.19 in³