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" 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) = r²(θ-sinθ)/2 ≅ 552.77 in² "

I am not clear on the following:

"chord"

"arcos"

"(θ-sinθ)"

Thanks.

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(½)

Since cos(π/3) = ½, arccos(½) = π/3.

θ = 2π/3

The central angle is 2π/3 radians.

area of segment = r²(θ-sinθ)/2

= 30²(2π/3 - sin(2π/3))/2

= 900(2π/3 - √3/2)/2

= 450(2π/3 - √3/2)

= 300π - 225√3

≅ 552.77 in²

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