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It is required to make a closed cylindrical tank of height \( 1 \mathrm{~m} \) and base diameter \( 140 \mathrm{~cm} \) from a metal sheet. How many square metres of the sheet are required for the same?
Given:
It is required to make a closed cylindrical tank of height $1\ m$ and base diameter $140\ cm$ from a metal sheet.
To do:
We have to find the area of the sheet required.
Solution:
Height of the cylinder $(h) = 1\ m$
$= 100\ cm$
Diameter of the cylinder $= 140\ cm$
This implies,
Radius $(r)=\frac{140}{2}$
$=70 \mathrm{~cm}$
Therefore,
Total surface area $=2 \pi r(h+r)$
$=2 \times \frac{22}{7} \times 70(100+70)$
$=440 \times 170$
$=74800 \mathrm{~cm}^{2}$
$=\frac{74800}{100 \times 100} \mathrm{~m}^{2}$
$=7.48 \mathrm{~m}^{2}$
Hence, the total surface area $7.48 \mathrm{~m}^{2}$.