If $S_1 \& S_2$ are the total surface area of a sphere and the curved surface area of the circumscribed cylinder, then $S_1:S_2$ is

A conical cap is filled with ice cream. The ice cream forms a hemispherical shape on its top. The radius of the hemisphere is equal to the height of the cone. If the height of the hemispherical part is $7 cm,$ the volume of the ice cream is

A cone is within the cylinder and cylinder is within a cube touch, by all vertical faces with the same base and height, then the ratio of their volume will be

A tent is cylindrical up to a $3 m$ height and conical shape. If the diameter of the base is $105 m$ and the slant height of the conical part is $53 m$, the total canvas used in making the tent is

A vessel is in the form of a right circular cylinder mounted on a hemisphere. If the radius of the hemisphere is $7 cm$ and the total height of the vessel is $13 cm$. The surface area of the vessel is 

A storage tank consists of a circular cylinder with a hemisphere adjoining at either end. If the diameter of the cylinder be $1.4 m$ and its length be $8 m$, the cost of painting it on the outside at the rate of $₹10 per m^2$ will be,

A cylinder is of height $31 cm$ and base radius $7 cm$. A hemisphere of radius equal to the base radius of the cylinder is cut off from one end and a cone of maximum height from the remaining part is also cut off. The curved surface area of the remaining part is

The top and bottom radii of a frustum of a cone are $6 cm \& 3 cm$, respectively. Its height is $8cm$. There is a conical cavity of height $3 cm \& 6 cm$ at the bottom. The amount of material in the solid is

In the figure shown, if $AD=5, DG=2 \& GH=4.$

What is the shortest distance between $E \& C?$