Oil barrel trig problem?
An oil storage tank in the form of a cylinder is buried underground lying horizontal. It measures 6 feet across in DIAMETER and 10 feet long. The oil in the tank is 2 feet deep. how much oil (cubic feet) is in the tank?
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Verified answer
Volume = L*A
vol = L * { pi r^2/2 - [x sqrt(r^2 - x^2) + r^2 arcsin(x/r) ] }
where L is the length and x is the distance from the center to the surface of the liquid. The principal angle in radians is used for arcsin.
Substitute L =10; x =3-2 =1 , r = 3
A = pi * 9 /2 - [ 1* sqrt ( 9-1) + 9 arc sin( 1/3)
= 3.14*4.5 - sqrt8 + 9( 0.34)
= 14.13 - 2.83 +3.06
= 14.36
V = L*A
= 10*14.36
= 143.6