Lateral surface area of a cuboid $= \ldots \ldots \ldots$

$A$ metallic ball of radius $9 \,cm$ is melted and recast into three metallic balls. If the radii of two balls are $1 \,cm$ and $6 \,cm$,find the radius of the third ball (in $cm$).

In a cylinder,if the radius is halved and the height is doubled,the volume will be

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 surface area of a sphere and the curved surface area of a hemisphere are equal. Find the ratio of their radii.

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.