Question

The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

Answer 1

volume of sphere=4/3pi r³=1/6pid³
volume of given cilinder=1/4pid³

Answer 2

We have to prove that the volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.
Proof:
Let's the diameter of the sphere = 12 cm
Radius of sphere = r = 12/2 = 6 cm
Volume of sphere = V = 4/3πr³
                                   = (4/3) (π) (6)³
                                   = 288 π
Let the height of the cylinder = h = 12 cm
Radius of cylinder = r = 6 cm
Volume of cylinder = πr²h
                              = π (6)² (12)
                              = 432 π
Now,
Volume of sphere : Volume of cylinder
                  288 π : 432 π
                         2 : 3
Hence proved.
Hopefully it will help you.
Thanks.