Volume of a Right Circular Cone

Find the weight of a solid cone whose base is of diameter $14\mathrm{cm}$ and vertical height $51\mathrm{cm},$ supposing the material of which it is made weighs $10 \mathrm{grams}$ per $\mathrm{cubic}$$\mathrm{cm}$.

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If h, S and V denote respectively the height, curved surface area and volume of a right circular cone, then $3\pi {\mathrm{Vh}}^3-{\mathrm{S}}^2{\mathrm{h}}^2+9{\mathrm{V}}^2$ is equal to

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If the base radius and the height of a right circular cone are increased by $20\%,$ then the percentage increase in volume is approximately

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If the heights of two cones are in the ratio of $1: 4$and the radii of their bases are in the ratio $4:1,$ then the ratio of their volumes is

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A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is

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The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height, is

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If the height and radius of a cone of volume $V$ are doubled, then the volume of the cone, is

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If the volumes of two cones are in the ratio $1: 4$ and their diameters are in the ratio $4:5,$ then the ratio of their heights, is

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If the radius of the base of a right circular cone is $3r$and its height is equal to the radius of the base, then its volume is

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A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio

The height of a conical vessel is$3.5 \mathrm{cm}.$ If its capacity is$3.3$ $\mathrm{litres}$of milk. Find its diameter of its base.

If the volume of a right circular cone of height $9 \mathrm{cm}$ is $48\pi {\mathrm{cm}}^3$. Find the diameter of its base(in $\mathrm{cm}$).

The height of a cone is $15 \mathrm{cm}$. If its volume is $500\pi {\mathrm{cm}}^3$, then find the radius of its base( in $\mathrm{cm}$).

A conical pit of top diameter $3.5 \mathrm{m}$ is $12 \mathrm{m}$ deep. What is its capacity in$\mathrm{kilolitres}$?

The volume of a right circular cone is $9856 {\mathrm{cm}}^3$. If the diameter of the base is $28 \mathrm{cm},$ find:

slant height of the cone.

The volume of a right circular cone is $9856 {\mathrm{cm}}^3$. If the diameter of the base is $28 \mathrm{cm},$ find:

 height of the cone

If the volume of a right circular cone with height $21 \mathrm{cm}$ and slant height $28 \mathrm{cm}$ is $k {\mathrm{cm}}^3$, find $k$.

Find the volume (in ${\mathrm{cm}}^3$) of a right circular cone with:

(i) radius $6 \mathrm{cm},$ height $7 \mathrm{cm}.$

Find the volume of a right circular cone with:

$\left(ii\right)$ radius $3.5 \mathrm{cm},$ height $12 \mathrm{cm}$

Find the volume of the largest right circular cone that can be fitted in a cube whose edge is $14 \mathrm{cm}.$