Find the curved surface area and the total surface area of a hemisphere with a radius of $14\, cm$.

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 $3 \, \text{cm}$.

Find the total surface area of a cylinder with diameter $28 \text{ cm}$ and height $50 \text{ cm}$. (in $\text{cm}^2$)

The areas of the three adjacent faces meeting at one vertex of a cuboid are $4000 \, cm^2$,$2000 \, cm^2$,and $3200 \, cm^2$ respectively. Find the dimensions and the volume of the cuboid.

$A$ 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?

State whether the following statement is True or False and justify your answer: If the radius of a cylinder is doubled and its height is halved,the volume will be doubled.