$A$ toy is in the form of a cone surmounted on a hemisphere. The radius of the cone as well as the hemisphere is $3.5\, cm$ and the total height of the toy is $15.5\, cm$. Find its total surface area (in $cm^2$).

The $TSA$ (Total Surface Area) of a $5$-rupee coin is given by the formula $\ldots \ldots \ldots . .$

$A$ metallic sphere with diameter $12 \, cm$ is melted and identical balls with radius $0.3 \, cm$ are produced. Find the number of balls produced.

The curved surface area of a cylinder is $132 \, cm^2$. If its height is $3 \, cm$,its diameter is $\dots \dots \dots \, cm$.

Write 'True' or 'False' and justify your answer:
The actual capacity of a vessel as shown in the figure is equal to the difference between the volume of the cylinder and the volume of the hemisphere.

The rainwater from a roof of dimensions $22 \, m \times 20 \, m$ drains into a cylindrical vessel having a base diameter of $2 \, m$ and a height of $3.5 \, m$. If the rainwater collected from the roof just fills the cylindrical vessel,find the rainfall in $cm$.