The diameter of a solid hemisphere is $7 \, cm$. Find its curved surface area and total surface area (in $cm^2$).

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 $\frac{1}{6} \pi r^3$.

The edge of a cube is $35\, cm$. Find the total surface area of the cube (in $cm^2$).

For a given cylinder,the diameter of the base is $7 \,cm$ and its height is $12 \,cm$. Find the curved surface area of a cylinder (in $cm^2$).

$A$ small village, having a population of $5000$, requires $130\, \text{litres}$ of water per head per day. The village has an overhead cuboidal tank measuring $20\, \text{m} \times 13\, \text{m} \times 10\, \text{m}$. For how many days will the water of this tank last?

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