1955 AHSME Problems/Problem 36

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Problem 36

A cylindrical oil tank, lying horizontally, has an interior length of $10$ feet and an interior diameter of $6$ feet. If the rectangular surface of the oil has an area of $40$ square feet, the depth of the oil is:

$\textbf{(A)}\ \sqrt{5}\qquad\textbf{(B)}\ 2\sqrt{5}\qquad\textbf{(C)}\ 3-\sqrt{5}\qquad\textbf{(D)}\ 3+\sqrt{5}\\ \textbf{(E)}\ \text{either }3-\sqrt{5}\text{ or }3+\sqrt{5}$

Solution (takes advantage of answer choices)

In order to complete the rectangle area of the oil tank, the chord on the circle must have a length of $4$. Since it's not the diameter $6$, there are two possible outcomes. The only choice that reflects this is $\boxed{\textbf{(E)}}$.

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