'Weekly Challenge 28: the Right Volume' printed from 
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 $1$?
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