If the tank is on end, then if the depth is d ft, the volume is
π*3^2*d = 9πd ft^3
So, if 2 ft deep, that's 18π=56.5 ft^3
However, if the tank is lying on its side, so the axis is horizontal, then we have to figure the area of a circular segment - the cross-section.
In that case, if the oil is d feet deep where 0<=d<=3, we have the area of oil in the cross-section is
a = 1/2 r^2 (θ-sinθ)
where cos(θ/2) = (r-d)/r
Here, with r=3 and d=2,
θ/2 = 2arccos(1/3) = 2.462
a = 9/2 (2.462-sin(2.462)) = 8.25
So, the volume is 8.25*20 = 165 ft^3
The level of oil in a storage tank buried in the ground can be found in much the same way as a dipstick is used to determine the oil level in an automobile crankcase. Suppose the ends of the cylindrical storage tank are radius of 3ft and the cylinder is 20ft long. Determine the volume of oil in the tank to the nearest cubic foot if the rod shows a depth of 2ft.
1 answer
1 answer