A cylinder lies within a cube touching all its vertical faces and a conelies inside the cylinder. If their heights are same with the same base,find the ratio of their volumes.

A cylinder lies within a cube touching all its vertical faces and a co

1.	A cylinder lies within a cube touching all its vertical faces and a conelies inside the cylinder. If their heights are same with the same base,find the ratio of their volumes.
Answer» Assume that the length of all edges of the cube=x unitsFormula for volume of cube=x³ cube unitDue an occurrence that the cylinder is within the cube &it touches all the vertices faces of the cube.Therefore radius of the base of the cylinder & cone & height of cylinder of a cone=xVolume of the cylinder=π×{x/2}²×x=22/7×x³/411/14x³ cube unitVolume of cone should be=1/3π{x/2)²×x=11/42 cubic unitRequired ratio=volume of cube:volume of cylinder:volume of cone=x³:11/14x³:11/42x³=42:33:11