Question

The ratio of volume of a cylinder : volume of cone : volume of hemisphere of same radius and same height is

• A. 1 : 2 : 3
• B. 2 : 3 : 1
• C. 3 : 1 : 2
• D. 1 : 1 : 1

Answer 1

The correct option is C 3 : 1 : 2

Let r is the radius of base and h is the height of the cylinder ,cone and hemisphere

As height of the hemisphere=Radius of the hemisphere

$\because h=r$

Volume of the cylinder$=\pi r^{2}h=\pi r^{2}r=\pi r^3$

Volume of a cone$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi r^{2}r=\frac{1}{3}\pi r^3$

Volume of the hemisphere$=\frac{2}{3}\pi r^3$

Volume of the cylinder:Volume of the cone:Volume of the hemisphere

$\Rightarrow \pi r^3:\frac{1}{3}\pi r^3:\frac{2}{3}\pi r^3$

$\Rightarrow 1:\frac{1}{3}:\frac{2}{3}$

$\Rightarrow 3:1:2$