Surface area of a sphere $= \ldots \ldots.$

Write True or False and justify your answer in each of the following:
If the radius of a cylinder is doubled and its curved surface area is not changed,the height must be halved.

Find the amount of water displaced by a solid spherical ball of diameter $4.2 \, cm$,when it is completely immersed in water. (in $, cm^3$)

$A$ metallic ball of radius $9 \,cm$ is melted and recast into three metallic balls. If the radii of two balls are $1 \,cm$ and $6 \,cm$,find the radius of the third ball (in $cm$).

$A$ conical tent is made from a piece of cloth with an area of $165 \, m^{2}$. The radius of the base of the tent is $5 \, m$.
$(i)$ If one student occupies an average of $\frac{5}{7} \, m^{2}$ of ground area,how many students can sit in the tent?
$(ii)$ Find the volume of the cone.

The surface area of a cube whose edge is $a$ is: (in $a^{2}$)