Re: Fuel Gage Problem
draw a circle of radius 10cm to represent the cross-section
draw a chord across below the centre to represent the liquid level
join the ends of the chord to the centre to form a triangle with angle A
the area of the liquid equals the area of the sector minus the area of the triangle
using radians as angle measure this is calculated as (A x radius squared / 2) minus (1/2 x radius squared x sinA)
this comes to 50A - 50sinA and is known to be a quarter of the tank cross-section or pi x radius squared / 4 or 25 x pi
this equation, because of the mixture of trig and non-trig can only be solved by calculator iteration (don't forget we are working in radians) and the answer is 2.31 radians
half this to get the half angle of the triangle and use 10 x cosine1.155 (calculator on radians) to find the vertical distance of the liquid level below the middle
subtracting this answer from 10 gives you the dipping measurement of 5.96
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