If the lateral surface area of a cylinder is $94.2 \, cm^2$ and its height is $5 \, cm$,then find the radius of its base. (in $, cm$)

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

$A$ lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is $7 \,mm$ and the diameter of the graphite is $1 \,mm$. If the length of the pencil is $14 \,cm$,find the volume of the wood and that of the graphite. (in $,cm^3$)

$A$ cube of side $4 \, cm$ contains a sphere touching its sides. Find the volume of the gap in between. (in $, cm^3$)

$A$ solid cube of side $12 \, cm$ is cut into eight cubes of equal volume. What will be the side of the new cube? Also,find the ratio between their surface areas.

The dimensions of a cuboid are in the ratio of $4: 3: 1$. If its total surface area is $3800 \, cm^{2}$,then find its volume in $cm^{3}$.