Question:
50 circular plates each of diameter 14 cm and thickness 0.5 cm are placed one above the other to form a right circular cylinder. Find its total surface area.
Solution:
We have 50 circular plates, each with diameter = 14 cm
That is, radius = 7 cm and thickness = 0.5 cm
These plates are stacked on top of one another.
So, the total thickness $=0.5 \times 50 \mathrm{~cm}=25 \mathrm{~cm}$
This is clearly a cylindrical arrangement.
We know,
Total surface area of a cylinder $=2 \pi r h+2 \pi r^{2}$
$=2 \pi r(h+r)$
$=2 \pi \times 7(25+7)$
$=448 \pi$
$=1408$
So, the total surface area of the given arrangement is $1408 \mathrm{~cm}^{2}$