Conic Contents

Determine the greatest cylinder that can be inscribed in a given cone.

The Doctrine and Application of Fluxions, Part I, Thomas Simpson, 1750

The answer is: if the cone has altitude \(a\) and base diameter \(b\), then the maximum inscribed cylinder will have height \(\dfrac{1}{3}a\) and diameter \(\dfrac{2}{3}b\)

Convergence