$3$ cubes of side $3, 4$ and $5$ $cm$ respectively,are melted to form a new cube. The side of the new cube is......$cm$

$3$ 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.........$cm$.

The height of a right circular cone and the radius of its circular base are $9 \, cm$ and $3 \, cm$ respectively. The cone is cut by a plane parallel to its base so as to divide it into two parts. The volume of the frustum (i.e.,the lower part) of the cone is $44 \, cm^3$. The radius of the upper circular surface of the frustum $\left(\text{taking } \pi = \frac{22}{7}\right)$ is

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?

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

The volume of a conical tent is $1232 \, m^3$ and the area of its base is $154 \, m^2$. Find the length of the canvas required to build the tent,if the canvas is $2 \, m$ in width. (in $m$) (Take $\pi = \frac{22}{7}$)