A cylinder circumscribes a sphere. The ratio of their volumes is:

The correct answer is Option (1) → 3 : 2

A cylinder that circumscribes a sphere fits round it tightly: its radius is the sphere's radius \(r\) and its height is the sphere's diameter \(2r\).

• Volume of the cylinder \(=\pi r^2\times2r=2\pi r^3\)

• Volume of the sphere \(\displaystyle =\frac{4}{3}\pi r^3\)

• Ratio \(\displaystyle =2:\frac{4}{3}=6:4=3:2\)