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

The length of a room is $12\, m$,width $8\, m$,and height $6\, m$. How many boxes will it hold if each box occupies $1.5\, m^3$ of space?

The radius of the base of a hollow cone is $8\, cm$ and its height is $15\, cm$. $A$ sphere of the largest possible radius is placed inside the cone. What is the ratio of the radius of the base of the cone to the radius of the sphere?

The portion of a ditch $48 \ m$ long, $16.5 \ m$ wide, and $4 \ m$ deep that can be filled with stones and earth available during the excavation of a tunnel, cylindrical in shape, of diameter $4 \ m$ and length $56 \ m$ is (Take $\pi = \frac{22}{7}$)

$A$ circular wire of radius $42 \, cm$ is cut and bent in the form of a rectangle whose sides are in the ratio $6:5$. Find the smaller side of the rectangle (in $cm$).

$A$ tank, $16 \, m$ long and $23 \, m$ wide contains water. How many cubic $m$ of water must be added to it to make the surface rise by $16 \frac{2}{3} \, cm$? (in $m^3$)