Write 'True' or 'False' and justify your answer:
$A$ solid cylinder of radius $r$ and height $h$ is placed over another cylinder of the same height and radius. The total surface area of the shape so formed is $4 \pi r h + 4 \pi r^2$.

(B) False.
The total surface area of a single cylinder with radius $r$ and height $h$ is given by $2 \pi rh + 2 \pi r^2$.
When one cylinder is placed on top of another cylinder of the same radius and height,the two circular faces (one from each cylinder) are hidden at the point of contact.
The new shape is a single cylinder with radius $r$ and total height $H = 2h$.
The total surface area of this new cylinder is the sum of its curved surface area and the areas of its two circular bases.
Total Surface Area $= 2 \pi r H + 2 \pi r^2 = 2 \pi r(2h) + 2 \pi r^2 = 4 \pi rh + 2 \pi r^2$.
Since $4 \pi rh + 2 \pi r^2 \neq 4 \pi rh + 4 \pi r^2$,the given statement is False.