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Advanced Math/Volume - Tank Follow-up


" The surface of the gasoline is a chord of height h = 30 inches.
The chord subtends a central angle of θ = 2arccos((r-h)/r) ≅ 2.09 radians.
area of the segment (the portion with gasoline) = r(θ-sinθ)/2 ≅ 552.77 in "

I am not clear on the following:





A chord is a line segment joining two points on a circle.

Arccosine is the inverse of the cosine function. If cosθ = a/b, then arccos(a/b) = θ.

(θ-sinθ): I forgot to mention that θ is in radians.

In your case, θ = 2arccos()
Since cos(π/3) = , arccos() = π/3.
θ = 2π/3
The central angle is 2π/3 radians.

area of segment = r(θ-sinθ)/2
= 30(2π/3 - sin(2π/3))/2
= 900(2π/3 - √3/2)/2
= 450(2π/3 - √3/2)
= 300π - 225√3
≅ 552.77 in

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