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QUESTION: I still don't understand the following:

"cosine function"

"cosθ"

"θ-sinθ)"

I'm sorry.

ANSWER: Cosine and sine are trigonometric functions. Have you started studying trigonometry yet?

---------- FOLLOW-UP ----------

QUESTION: I didn't take trigonometry.

Okay, I'll use geometry to get to the same result.

The radius is 30 and the height of the gasoline is 15. The distance from the center of the circle to the top of the gasoline is 15 inches. See the right triangle.

By the Pythagorean theorem, the base of the triangle is 15√3. The ratio of the three sides tells you that it is a 30-60-90 triangle.

Area of the triangle = ½·15√3·15 = 112.5√3 in²

The area of the 60° sector = ⅙(area of the circle) = ⅙π30² = 150π in².

Shaded area = 150π - 112.5√3 ≅ 276.38

Volume of gasoline = 2·276.38·300 = 165829.91 in³

The rest is the same.

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