Find the total surface area of a hemisphere of radius $42 \, cm$. (in $cm^2$)

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

The length of the longest pole that can be placed in a room of dimensions $(10 \text{ m} \times 10 \text{ m} \times 5 \text{ m})$ is (in $\text{m}$):

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

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.

The volume of a solid cylinder is $4620 \, cm^{3}$ and its radius is $7 \, cm$. Find its height in $cm$.