A cylinder of height 2 m and radius 2 m is partially filled with oil. When the cylinder is lying parallel to the ground the height of oil level is 1.5 m from ground. What is the volume of oil? How to solve it? I didn't find any similar questions. If this is a duplicate, kindly give me the link to that post. Thanks in advance.
2026-03-28 12:49:13.1774702153
Finding the volume of oil in a cylinder which is lying parallel to the ground.
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If you draw a circle of radius $2$ and a horizontal chord at a height of $1.5$ above the bottom of the circle, then this chord is $0.5$ below the centre of the circle. We need to find the area of the segment below the chord and multiply this by the length of the cylinder, $2$.
The area of the segment is $$\frac 12(2)^2(\theta-\sin \theta),$$ where $\theta=2\arccos(\frac{0.5}{2})$ measured in radians.
You should be able to get the answer now.