Volume and Total Surface Area of Right Circular Cone

The diameter of the base of a right circular cone is $6 \mathrm{cm}$ and its perpendicular height is $3\sqrt{3} \mathrm{cm}$. Find the slant height of the 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.

A conical tent with base-radius$7 \mathrm{m}$ and height $24 \mathrm{m}$ is made from $5 \mathrm{m}$ wide canvas. The length of the canvas used is

The height of a cone is $30 \mathrm{cm}$. A small cone is cut off at the top by a plane parallel to, its base. If its volume is $\frac{1}{27}$ of the volume of the  given cone. then what is the height of the frustum of the cone ?

A tub is in the shape of a frustum of a cone. The radii of two circular ends of the tub are $105 \mathrm{cm}$ and $42 \mathrm{cm}$. If the vertical height of the tub is $16 \mathrm{cm}$, what is its slant height ?

A right angle whose sides are $15 \mathrm{cm}$ and $20 \mathrm{cm}$ is made to revolve about its hypotenuse. The volume of the double cone so formed is:

Four pipes of each of $5 \mathrm{cm}$ in diameter are to be replaced by a single pipe discharging the same quantity of water. If the speed of water remains same in both the cases, then the diameter of the single pipe

Find the total surface area and curved surface area of the cone whose radius is $7 \mathrm{cm}$ and slant height is $3 \mathrm{cm}$. (Use π = 22/7).

What is the height of the cone with the radius $= 3$ units and volume $= 50$ cubic units?

Determine the curved surface area of a cone whose base radius is $7 \mathrm{cm}$ and slant height is $15 \mathrm{cm}$.

Which shape is formed by rotating a right triangle about its height or altitude?

Identify the cone from the following shapes:

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 _____.
 

A cone is inscribed in a sphere of radius $8$so that the slant height of the cone is exactly twice the length of the radius of the cone. What is the largest possible value for the volume of such a cone?

A right triangle with legs $5$ cm and $12$ cm is rotated $360°$ about its hypotenuse. The surface area of the formed solid is $k\frac{60\pi }{13}$. What is value of $k$?

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 $k$?