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

$A$ cylindrical roller $2.5\, m$ in length and $1.75\, m$ in radius,when rolled on a road,was found to cover an area of $5500\, m^{2}$. How many revolutions did it make?

The radius and volume of a cylinder are $3.5\,cm$ and $2310\,cm^3$ respectively. Find its height in $cm$.

The total surface area of a cone whose radius is $\frac{r}{2}$ and slant height is $2l$ is

$30$ 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.

Write True or False and justify your answer in each of the following: If the length of the diagonal of a cube is $6 \sqrt{3} \, \text{cm}$,then the length of the edge of the cube is $3 \, \text{cm}$.