If the radius of a cylinder is doubled and the height is halved,then what would be the ratio between the new curved surface area and the previous curved surface area of the cylinder?

$A$ 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?

The diameter of a copper sphere is $18 \, cm$. The sphere is melted and drawn into a long wire of uniform circular cross-section. If the length of the wire is $108 \, m$,the diameter of the wire is ....... $cm$.

From a cubical block of wood of side $1 \, m$,a cylinder of the largest possible volume is carved out. The volume (in $m^3$) of the remaining wood is

Three spherical balls of radius $2 \, cm$,$4 \, cm$,and $6 \, cm$ are melted to form a new spherical ball. In this process,there is a loss of $25 \%$ of the material. What is the radius (in $cm$) of the new ball?

$A$ solid right circular cone of radius $4\, cm$ and height $7\, cm$ is placed inside a cylindrical vessel of radius $5\, cm$ and height $8\, cm$. How much water (in $cm^3$) will be required to fill the cylindrical vessel completely?