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:
$A$ solid cone of radius $r$ and height $h$ is placed over a solid cylinder having the same base radius and height as that of the cone. The total surface area of the combined solid is $\pi[\sqrt{r^{2}+h^{2}}+3r+2h]$.

Two identical cubes each of volume $64 \, cm^{3}$ are joined together end to end. What is the surface area of the resulting cuboid? (in $cm^{2}$)

Which of the following correctly matches the information given in Part $I$ and Part $II$?

Part $I$	Part $II$
$1.$ Volume of a cuboid	$a.$ $\frac{1}{3} \pi r^{2} h$
$2.$ Volume of a cone	$b.$ $\pi r^{2} h$
$3.$ Volume of a cylinder	$c.$ $\frac{4}{3} \pi r^{3}$
$4.$ Volume of a sphere	$d.$ $lbh$

Total surface area of a cylinder $= \dots$

$A$ cylinder is closed at both ends by $40 \, cm$ high cones. The radius of the cylinder is $30 \, cm$ and the total height of the article is $180 \, cm$. Find the total surface area of the article. $(\pi = 3.14)$ (in $cm^2$)