The total surface area of a hemisphere is $4158 \, cm^2$. Find its diameter in $cm$.

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.

Surface area of a cuboid = $\ldots \ldots \ldots$

$1 \, m^{2} = \ldots \ldots \, cm^{2}$

The dimensions of a cuboidal box are in the ratio $6: 4: 3$. The difference between the cost of covering it with white paper at the rate of $₹ 2.00$ per $m^2$ and with coloured paper at the rate of $₹ 2.50$ per $m^2$ is $₹ 1350$. Find the dimensions of the box.

The surface area of a sphere is $5544 \, cm^2$. Find its volume in $cm^3$.