What will be the ratio of the volumes of a solid cone , a solid hemisphere and a solid cylinder when their radii of bases and heights are equal ?

Explanation

Let radius of the cone , hemisphere and cylinder be r unit and their equal heights be h unit .
Since the heights of the three objects are equal ,
` :. ` height of the cone = height of the cylinder = height of the hemisphere = radius of the hemisphere : volume of the cylinder
` = 1/3 pir^(2) h : 2/3 pir^(3) : pir^(2) h `
` = 1/3 pi r^(2) . r , 2/3 pir^(3) : pir^(2) r `
` = 1/3 pi r^(3) : 2/3 pir^(3) : pir^(3) `
` = 1/3 : 2/3 : 1 `
= 1: 2 : 3
Hence the required ratio is 1 : 2 : 3