Weekly Challenge 28: the Right Volume

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A segment of the curve $y=f(x)$ starts at $(0, 0)$ and ends at $(1, 1)$. It is rotated about the $x$ axis to form a volume. Can you find a curve which will result in a volume of $1$?

Did you know ... ?

That volumes of revolution are often used in mechanics calculations. They were used by Archimedes around 250 BC to calculate volumes of solids created by rotating conic sections about an axis.