Write True or False and justify your answer: The volume of a sphere is equal to two-thirds of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

(A) Let the radius of the sphere be $r$.
Given that the height and diameter of the cylinder are equal to the diameter of the sphere.
Since the diameter of the sphere is $2r$,the height of the cylinder $h = 2r$ and the diameter of the cylinder is $2r$.
Therefore,the radius of the cylinder is $r$.
Volume of the sphere $= \frac{4}{3} \pi r^3$.
Volume of the cylinder $= \pi r^2 h = \pi r^2 (2r) = 2 \pi r^3$.
Two-thirds of the volume of the cylinder $= \frac{2}{3} \times (2 \pi r^3) = \frac{4}{3} \pi r^3$.
Since the volume of the sphere is equal to $\frac{4}{3} \pi r^3$,the statement is True.