The radii of three metallic spheres are $3 \, cm$,$4 \, cm$,and $5 \, cm$. These spheres are melted and recast into a single new sphere. Find the radius of the new sphere (in $cm$).

Write 'True' or 'False' and justify your answer:
The volume of the frustum of a cone is $\frac{1}{3} \pi h[r_{1}^{2} + r_{2}^{2}-r_{1} r_{2}],$ where $h$ is the vertical height of the frustum and $r_{1}, r_{2}$ are the radii of the ends.

The volume of a sphere is $4.5 \pi \, cm^3$. Then,its diameter is $\ldots \ldots \ldots \ldots cm$.

The radii of the ends of a frustum of a cone of height $h \text{ cm}$ are $r_{1} \text{ cm}$ and $r_{2} \text{ cm}$. The volume in $\text{cm}^{3}$ of the frustum of the cone is:

Total surface area of a hemisphere with diameter $2 \, cm$ is $\ldots \ldots \ldots cm^{2}$.

$A$ cylinder with radius $6 \, cm$ is closed at one end by a $8 \, cm$ high cone and is open at the other end. The total height of the article is $20 \, cm$. Find the total surface area of the article. $(\pi = 3.14)$ (in $cm^2$)