Finding the volume of oil in a cylinder which is lying parallel to the ground.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?

Question

Bradley Sherman · Accepted Answer

Step 1If 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.Step 2The area of the segment is      1    2    (  2      )    2    (  θ  −  sin  ⁡  θ  )  ,, where   θ  =  2  arccos  ⁡  (      0.5    2    ) measured in radians.You should be able to get the answer now.

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?

Answered question

Answer & Explanation

New Questions in High school geometry