Volume of a Right Circular Cone

A Semi-circular piece of paper of radius $r \mathrm{cm}$ is folded to from a cone. The volume of the cone thus formed is _____${\mathrm{cm}}^3$.

The radii of a right circular cone and a right circular cylinder are in the ratio $4:3$ and their heights are in the ratio $2:3$. The ratio of their volumes is

A cone, hemisphere and cylinder stand on equal bases and have the same height then the ratio of their volumes is _____.
 

Height of a right cone is twice that of another cone and radius of the base of the first cone is half of that of the second cone. What is the ratio of their volumes?

When a right cone is cut through a slant height and opened, the central angle of the formed sector is ${60}^{°}$ and curved area of the cone is $\frac{3\pi }{2} c{m}^2$. The volume of cone is $k\pi$. What is value of $k$?

The slant height of a right cone is $6 cm$ and makes $60°$ angle with the base. The volume of the cone is $k\sqrt{3}\pi$. What is the value of $k$.
 

If the height and the radius of the cone are doubled, then the volume of the cone becomes

 What is the volume of $x$ in terms of $r$ and $h$? If the volume of liquid is $\frac{\pi }{3}x²(r+h)$. What is the value of $x$?