A cylinder is within the cube touching all the vertical faces. A cone is inside the cylinder. If heights are some with the same base, find the ratio of their volumes.

Explanation

Let the length of each edge of the cube be `x` units.
`V_1=`Volume of the cube`=x^3`
For cylinder,
Radius of the cylinder`=x/2`
Height of the cylinder`=x`
`V_2=`Volume of the cylinder`=pir^2h`
`=22/7xx\x/2xx\x/2xx\x` cubic units
`=11/14x^3`.
For cone,
`V_3=`Volume of the cone`=pir^2h`
`=1/3xx11/14x^3` cubic units
`=11/42x^3` cubic units
`:.`Required ratio`=V_1:V_2:V_3`
`=x^3:11/14x^3:11/42x^3`
`=42:33:11`
Hence, the ratio is `42:33:11`.