29.A cylinder is within the cube touching all the vertical faces. A cone isinside the cylinder. If their height are the same with the same base. Findthe ratio of their volumes.

29.A cylinder is within the cube touching all the vertical faces. A co

1.	29.A cylinder is within the cube touching all the vertical faces. A cone isinside the cylinder. If their height are the same with the same base. Findthe ratio of their volumes.
Answer» Let the length of each edge of the cube beaunits.∴ Volume of cube =a^3cube unitsSince the cylinder is within the cube and it touches all the vertical faces of cube.∴ Radius of base of the cylinder and the cone= (a/2) unitsHeight of the cylinder and the cone =a unitsVolume of cylinder = πr^2h=π(a/2)^2x a = (22/7) x (a^2/4) x a= (11/14)a^3Volume of cone = (1/3)πr^2h= (1/3) xπ(a/2)^2x a = (22/21) x (a^2/4) x a= (11/42)a^3Consider, volume of cube : volume of cylinder : volume of cone = a^3: (11/14)a^3: (11/42)a^3= 1 : (11/14) : (11/42)= 42 : 33 : 11