Solution:
(i)Let the radius of sphere be r.
Then height of the cylinder, h = 2r
Radius of cylinder = r
Volume of cylinder = r2h
= ×r2×2r
= 2r3
Volume of sphere = (4/3)r3
= (2/3)× 2r3
= (2/3)× Volume of cylinder
Hence the given statement is true.
(ii)Let the edge of the cube is 2r.
So radius of cone = r
Height of cone, h = 2r
Volume of cone = (1/3)r2h
= (1/3)r2×2r
= (2/3)r3
= Volume of a hemisphere of radius r
Hence the given statement is true.
(iii)Let r be radius of cone, hemisphere and cylinder.
So the height of the cone = r
Height of cylinder = r
Volume of cone = (1/3)r2h
= (1/3)r3
Volume of hemisphere = (2/3)r3
Volume of cylinder = r2h
= r3
Ratio of volume of cone , hemisphere and cylinder = (1/3)r3 : (2/3)r3 : r3
= 1/3 : 2/3 : 1
= 1:2:3
Hence the given statement is true.