50 circular plates each of diameter $ 14 \mathrm{~cm} $ and thickness $ 0.5 \mathrm{~cm} $ are placed one above the other to form a right circular cylinder. Find its total surface area.

Given:

50 circular plates each of diameter \( 14 \mathrm{~cm} \) and thickness \( 0.5 \mathrm{~cm} \) are placed one above the other to form a right circular cylinder.

To do:

We have to find its total surface area.

Solution:

Diameter of each circular plate $= 14\ cm$

This implies,

Radius of each circular plate $r = \frac{14}{2}$

$= 7\ cm$

Thickness of each circular plate $h = 0.5\ cm$

Height of 50 plates placing one above the other $H= 0.5 \times 50$

$= 25\ cm$

Curved surface area of the cylinder so formed $= 2 \pi rH$

$= 2 \times \pi \times 7 \times 25$

$= 350 \pi\ cm^2$

Total surface area $= 350 \pi + 2 \times \pi r^2$

$=350\times\frac{22}{7}+ 2 \times \frac{22}{7} \times 7^2$

$= 1100 + 308$

$= 1408\ cm^2$

The total surface area is $1408\ cm^2$. 

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Updated on: 10-Oct-2022

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