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Central Angle and Depth Relation Calculus

how is the relationship between the central angle theta and the depth of an amount of liquid in a cylinder tank on its side h= r(1-cos(theta/2)?

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Daniel O. | Math and Physics Tutor, with a math and physics degreeMath and Physics Tutor, with a math and ...
5.0 5.0 (265 lesson ratings) (265)

The picture might help:

cos(α/2) = (r-h)/r

r*cos(α/2) = r-h

h = r - r*cos(α/2) = r(1 - cos(α/2))

h = r(1 - cos(α/2))

Hopefully that helps.

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)

Your formula h= r(1-cos(theta/2) is correct if the liquid level is below the center of the tank.

If the liquid level is above the center of the tank, the formula should be h= r(1+cos(theta/2)