A hemisphere is inscribed in a cylinder and a cone is inscribed in the hemisphere .The vertex of cone lies on the centre of the upper circular part of the cylinder .Show that , `(1)/(3)xx`Volume of cylinder =`(1)/(2) xx`Volume of hemishphere= Volume of cone

Explanation

Let radius of cone = radius of cylinder = radius of hemisphere= r
Height of cone = Height of cylinder = r
Now the volume of cone =`(1)/(3)pir^(2).(r)=(1)/(3)pir^(3)`
volume of hemisphere=`(2)/(3)pir^(3)`
`(1)/(2)xx`volume of hemisphere=`(1)/(3)pir^(3)`
and volume of cylindr =`pir^(2)(r)=pir^(3)`
`(1)/(3)xx` volume of cylinder = `(1)/(3)pir^(3)`
From equatioopns (1),(2)and (3)
`(1)/(3)xx` volume of cylinder `= (1)/(2)xx` volume of hemishpere
=volume of cone