Volume of a Right Circular Cone

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

The circumference of the base of a $12 \mathrm{m}$ height solid cone is $22 \mathrm{m}$. Find the volume of the cone.

If the height of two cones are in the ratio 1$1:3$ and the radii of their bases are in the ratio $4:1$, then what is the ratio of their volume?

If the volume of a cone whose radius is $8 \mathrm{cm}$ and height is $12 \mathrm{cm}$ is $k {\mathrm{cm}}^3$

Then find the value of $k$ correct to two decimal places.

The volume of a right circular cone height $12 \mathrm{cm}$ is $68\pi {\mathrm{cm}}^3$. If the diameter of its base is $\mathrm{k}\sqrt{17}$, then write the value of $\mathrm{k}$.

Find the value of $a$ if the volume $\left(\mathrm{in} {\mathrm{cm}}^3\right)$ of the right circular cone with radius $3.5 \mathrm{cm}$, height $12 \mathrm{cm}$ is given by $a {\mathrm{cm}}^3$. (Assume $\mathrm{\pi }=\frac{22}{7}$)

Find the volume $\left(\mathrm{in} {\mathrm{cm}}^3\right)$ of the right circular cone with radius $6 \mathrm{cm}$, height $7 \mathrm{cm}$. (Assume $\mathrm{\pi }=\frac{22}{7}$)

 A right cylindrical vessel is full with water. How many right cones having the same diameter and height as those of the right cylinder will be needed to store that water?
 

If the height of two cones are in the ratio 1$1:3$ and the radii of their bases are in the ratio $4:1$, then what is the ratio of their volume?

A metallic right circular cone of height $9 \mathrm{cm}$ and base radius $7 \mathrm{cm}$ is melted and recast into a cuboid whose two sides are $11 \mathrm{cm}$ and $6 \mathrm{cm}$. Then the third side of the cuboid is

The volume of the largest circular cone that can be cut from a cube whose edge is $8 \mathrm{cm}$ is

If the height of a cone is doubled, then its volume is increased by

In the given figure, a right circular cone of diameter $r \mathrm{cm}$ and height $12 \mathrm{cm}$ rests on the base of a right circular cylinder of radius $r \mathrm{cm}$. Their bases are in the same plane and the cylinder is filled with water upto a height of $12 \mathrm{cm}$. If the cone is removed, then find the height to which water level will fall. 

Find the volume of a cone whose radius is $8 \mathrm{cm}$ and height is $12 \mathrm{cm}$.

If the volume of a right circular cone of height $12 \mathrm{cm}$ is $68\mathrm{\pi } {\mathrm{cm}}^3$. Find the diameter of its base.