The ratio between volume of a sphere and volume of a circumscribing right circular cylinder is: 

Given:

The ratio between volume of a sphere and volume of a circumscribing right circular cylinder is:

Formula used:

Volume of a sphere = \(\dfrac{4}{3}\pi r^3\)

Volume of a circumscribing right circular cylinder = \(\pi r^2 \times 2r\)

Calculation:

Volume of a sphere = \(\dfrac{4}{3}\pi r^3\)

Volume of a cylinder = \(\pi r^2 \times 2r = 2\pi r^3\)

⇒ Ratio = \(\dfrac{\dfrac{4}{3}\pi r^3}{2\pi r^3}\)

⇒ Ratio = \(\dfrac{\dfrac{4}{3}}{2}\)

⇒ Ratio = \(\dfrac{2}{3}\)

∴ The correct answer is option (3).