Cone

A hollow sphere of internal and external radii $6 \mathrm{cm} \& 8 \mathrm{cm}$ respectively, is melted and recast into small cones of base radius $2 \mathrm{cm}$ and height $8 \mathrm{cm}$. Find the number of cones.

The radius of the base of a conical tent is $3.5$ m and the height is $12$ m. Neglecting the thickness of the cloth wall, find the total cost of spraying disinfectants on the outer and inner walls and floor of the tent if $₹ 2.5$ is spent per square meter.

Find the difference between the entire surface and the curved surface of a cone of base radius 5 cm.

The bottom of a right cylindrical shaped vessel made from metallic sheet is closed by a cone-shaped vessel as shown in the figure. The radius of the circular base of the cylinder and radius of the circular base of the cone are each is equal to $7 \mathrm{cm}$. If the height of the cylinder is $20 \mathrm{cm}$ and height of cone is $3 \mathrm{cm}$, calculate the cost of milk (in $₹$) to fill completely this vessel at the rate of $₹20$ per litre. [Take $\mathrm{\pi }=\frac{22}{7}$]

The radius and slant height of a cone are $4 \mathrm{cm}$ and $25 \mathrm{cm}$ respectively. Find the curved surface area of that cone in $\mathrm{cm}$.$\left(\mathrm{\pi }=3.14\right)$

Perpendicular height of a cone is $12 \mathrm{cm}$ and its slant height is $13 \mathrm{cm}$. Find the radius of the base of cone in $\mathrm{cm}$.

Volume of a right circular cone is

The total surface area of a cone whose radius is $r$ and slant height is $l$ is

Find the total surface area (in ${\mathrm{m}}^2$) of cone whose diameter of base is $14 \mathrm{m}$ and slant height is $25 \mathrm{m}$. Assume $\mathrm{\pi }=\frac{22}{7}$.

The radius of a sector is $12 \mathrm{cm}$ and angle is $120°$. By coinciding its straight sides, a cone is formed. Find the volume of that cone.

A cone of maximum height is cut from a cube of edge $14 \mathrm{cm}$. Find the volume of the cone.

The circumference of the base of a conical tent is $9 \mathrm{m}$ and height is $44 \mathrm{m}$. Find the volume of air inside it in ${\mathrm{m}}^3$.

The ratio of slant height and radius of a cone is $7:4$. If its curved surface area is $792 {\mathrm{cm}}^2$, then find its radius in $\mathrm{cm}$.

The bases of two cones are of the same diameter. Ratio of their slant heights is $5:4$. If curved surface area of the smaller cone is $400 {\mathrm{cm}}^2$, then find the curved surface area of the bigger cone in ${\mathrm{cm}}^2$.

Find the height$\left(\mathrm{in} \mathrm{cm}\right)$of the right circular cone of slant height $25 \mathrm{cm}$ and area of its base is $154 {\mathrm{cm}}^2$.

Find the total surface area of cone in ${\mathrm{m}}^2$, whose diameter of base is $14 \mathrm{m}$, and slant height is $25 \mathrm{m}$.

Find the slant height of the right circular cone in $\mathrm{cm}$, whose volume is $1232 {\mathrm{cm}}^3$ and height is $24 \mathrm{cm}$.