$A$ room without a ceiling is $12 \, m$ long,$4 \, m$ wide,and $3 \, m$ high. Find the length of the longest rod that can be placed in that room. (in $m$)

If the edge of a cube is $7\, cm$,find its total surface area in $cm^2$.

The circumference of the base of a cylindrical vessel is $132 \,cm$ and its height is $25 \,cm$. How many litres of water can it hold (in $,l$)? $(1000 \,cm^3 = 1 \,l)$ Assume $\pi = \frac{22}{7}$.

$A$ school provides milk to the students daily in cylindrical glasses of diameter $7 \, cm$. If the glass is filled with milk up to a height of $12 \, cm$, find how many litres of milk is needed to serve $1600$ students.

$A$ right circular cylinder just encloses a sphere of radius $r$ (see figure). Find:
$(i)$ Surface area of the sphere,
$(ii)$ Curved surface area of the cylinder,
$(iii)$ Ratio of the areas obtained in $(i)$ and $(ii)$.

$A$ child is playing with building blocks, which are in the shape of cubes, and has built a structure as shown in the figure. If the edge of each cube is $3 \, cm$, find the volume of the structure built by the child. (in $cm^3$)