A solid cylinder has total surface area of $462 {\mathrm{cm}}^2.$ Its curved surface area is one-third of its total surface area. Find the radius and height of the cylinder.

A soft drink is available in two packs $-$ (i) a tin can with a rectangular base of length $5 \mathrm{cm}$ and width $4 \mathrm{cm},$ having a height of $15 \mathrm{cm}$.

(ii) A plastic cylinder with circular base of diameter $7 \mathrm{cm}$ and height $10 \mathrm{cm}.$ Which container has greater capacity and by how much? 

If the lateral surface area of a cylinder is $94.2 {\mathrm{cm}}^2$ and its height is $5 \mathrm{cm}$, then the radius of its base is $k \mathrm{cm}$. Find $k$.

If the lateral surface area of a cylinder is $94.2 {\mathrm{cm}}^2$ and its height is $5 \mathrm{cm}$, If the volume of the cylinder is $k {\mathrm{cm}}^3$, find $k$ (up to one decimal place). Take $\mathrm{\pi }=\frac{22}{7}$.