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'Weekly Challenge 28: the Right Volume' printed from http://nrich.maths.org/
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
about an axis.