$3$ spherical balls of radii $1\, cm$,$2\, cm$,and $3\, cm$ are melted to form a single spherical ball. In the process,the loss of material is $25\%$. The radius of the new ball is.........$cm$.

$A$ hemisphere is made of lead. Its radius is $6 \, cm$. It is cast into a right circular cone of $75 \, cm$ height. The radius of the base of the cone is ......... $cm$.

$A$ $3.3\, m$ high room is half as long again as it is wide and its volume is $123 \frac{3}{4}\, m^3$. Find its length and breadth.

$A$ hollow hemispherical bowl is made of silver with its outer radius $8\, cm$ and inner radius $4\, cm$. The bowl is melted to form a solid right circular cone of radius $8\, cm$. The height of the cone formed is......$cm$

The respective ratio of the curved surface area and total surface area of a cylinder is $4:5$. If the curved surface area of the cylinder is $1232 \, cm^2$,what is the height? (in $cm$)

$A$ solid cone of height $24 \, cm$ and base radius $8 \, cm$ is melted to form a solid cylinder of radius $6 \, cm$ and height $6 \, cm$. In the whole process,what percent of material is wasted (in $\%$)?