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# help

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A right cylindrical oil tank is 15 feet tall and its circular bases have diameters of 4 feet each. When the tank is lying flat on its side (not on one of the circular ends), the oil inside is 3 feet deep. How deep, in feet, would the oil have been if the tank had been standing upright on one of its bases? Express your answer as a decimal to the nearest tenth.

Jan 1, 2019

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We  will  need to use Calculus to solve this.....

Looking at the circular cross section of the cylinder, it can be expressed as  a circle with a radius of 2 centered at the origin......its equation is :

x^2 + y^2 =  4

....so....

y =  √ [ 4 - x^2 ]

The area of the circle covered by the oil is given by

Area of circle - area not covered by the oil  =

√3

pi * (2)^2  -    ∫   √[ 4 - x^2]  -  1   dx        ≈ 10.1096   ft^2

-√3

So...the volume of the oil is

Area covered by oil * cylinder height  = 10.196 * 15   =  151.644 ft^2

So....the height of the oil when the tank is upright can be found as

151.644 =   pi * (2)^2 * height

151.644 =  4 pi * height        divide both sides by   4 pi

151.644 / [ 4 pi ]   = height ≈    12.1 ft   Jan 1, 2019
edited by CPhill  Jan 1, 2019