The curved surface area of a cylinder is $550 \, cm^2$. If its height is $50 \, cm$,find its diameter in $cm$.

State whether the following statement is true or false:
An open box measuring $12\, cm \times 4\, cm \times 3\, cm$ can hold a bar of $15\, cm$ in length.

In a hot water heating system,there is a cylindrical pipe of length $28 \, m$ and diameter $5 \, cm$. Find the total radiating surface in the system. $\left[ \text{Assume } \pi = \frac{22}{7} \right]$ (in $, m^2$)

$1 \, m^3 = \dots \dots$ litre

$A$ 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.

$30$ circular plates,each of radius $14\,cm$ and thickness $3\,cm$,are placed one above the other to form a cylindrical solid. Find:
$(i)$ the total surface area
$(ii)$ the volume of the cylinder so formed.