How many small cubes,each of $96\,cm^{2}$ surface area,can be formed from the material obtained by melting a larger cube with $384\,cm^{2}$ surface area?

$A$ right circular cylinder having diameter $21\, cm$ and height $38\, cm$ is full of ice cream. The ice cream is to be filled in cones of height $12\, cm$ and diameter $7\, cm$ having a hemispherical shape on the top. The number of such cones to be filled with ice cream is

The volume of a solid cylinder whose base diameter is $14\, mm$ and length is $25\, mm$ is $3850\, mm^3$. If the length of the cylinder is doubled but the diameter is halved,what will be the volume of the resulting cylinder? (in $mm^3$)

$X$ and $Y$ are two cylinders of the same height. The base of $X$ has a diameter which is equal to half the diameter of the base of $Y$. If the height of $X$ is doubled,the volume of $X$ becomes

The radius of the base of a solid cone is $9\, cm$ and its height is $21\, cm$. It is cut into $3$ parts by two cuts which are parallel to its base. The cuts are at heights of $7\, cm$ and $14\, cm$ from the base respectively. What is the ratio of the curved surface areas of the top,middle,and bottom parts respectively?

The radius and height of a right circular cone are in the ratio $3: 4$. If its volume is $96\pi\, cm^3$,what is its slant height (in $cm$)?