If the edge of a cube is $7\, cm$,find its total surface area in $cm^2$.

The radius of a sphere is $3.5\, cm$. Find the cost of plating gold on its surface at the rate of ₹ $150$ per $cm^{2}$. (in ₹)

Write True or False and justify your answer.
An edge of a cube measures $r \, cm$. If the largest possible right circular cone is cut out of this cube,then the volume of the cone (in $cm^3$) is $\frac{1}{6} \pi r^3$.

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 $3 \, \text{cm}$.

$A$ 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 $cm$).

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