50 circular plates each of diameter 14 cm and thickness 0.5 cm

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 $1408 \mathrm{~cm}^{2}$

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