If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio o

Question

If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of cone hollowed out is\

Professor PC Thomas Classes · Answer

(c) : Let $r$ and $h$ be the radius and height of cylinder respectively.\ Volume of cone hollowed out $=\frac{1}{3} \pi r^{2} h$\ Volume of remaining wood = Volume of cylinder - Volume of cone\ \ $=\pi r^{2} h-\frac{1}{3} \pi r^{2} h=\frac{2}{3} \pi r^{2} h$\ ∴ Required ratio $=\frac{\frac{2}{3} \pi r^{2} h}{\frac{1}{3} \pi r^{2} h}=\frac{2}{1}=2: 1$