Find the curved surface area (in $cm^{2}$) of a hemisphere of diameter $28\, cm$.

$A$ ball of lead,$4\, cm$ in diameter,is covered with gold. If the volume of the gold and lead are equal,then the thickness of gold is approximately (in $cm$).
$[$ Given $\sqrt[3]{2} = 1.259 ]$

The ratio of the curved surface area and volume of a cylinder is $1:7$. The ratio of the total surface area and volume is $187:770$. What is the ratio of its base radius to its height?

$A$ semicircular sheet of metal of diameter $28 \, cm$ is bent into an open conical cup. The capacity of the cup (taking $\pi = \frac{22}{7}$) is (in $cm^3$):

The base of a $10\, cm$ high solid cylinder is a semi-circle of radius $7\, cm$. Its total surface area (in $cm^2$) is (Use $\pi = \frac{22}{7}$)

$A$ school room is to be built to accommodate $70$ children,so as to allow $2.2\, m^2$ of floor area and $11\, m^3$ of space for each child. If the room is $14\, m$ long,what must be its breadth and height?