The capacity of a closed cylindrical vessel of height $1\ m$ is $15.4$ litres. How many square metres of metal sheet would be needed to make it?

 Given:

The capacity of a closed cylindrical vessel of height $1\ m$ is $15.4$ litres.

To do:

We have to find the metal sheet needed to make the vessel.

Solution:

The capacity of the closed cylindrical vessel $= 15.4\ L$

This implies,

Volume of the vessel $=\frac{15.4}{1000}$

$=0.0154 \mathrm{~m}^{3}$                    (Since $1\ m^3=1000\ L$)

$=0.0154 \times 100 \times 100 \times 100\ cm^3$

$=15400 \mathrm{~cm}^{3}$

Height of the vessel $(h)=1 \mathrm{~m}$

$=100 \mathrm{~cm}$

Therefore,

Radius of the cylindrical vessel $=\sqrt{\frac{\text { Volume }}{\pi h}}$

$=\sqrt{\frac{15400 \times 7}{22 \times 100}}$

$=\sqrt{49}$

$=7 \mathrm{~cm}$

This implies,

Total surface areaof the cylindrical vessel $=2 \pi r(h+r)$

$=2 \times \frac{22}{7} \times 7(100+7)$

$=44 \times 107$

$=4708 \mathrm{~cm}^{2}$

$=\frac{4708}{100 \times 100}\ m^2$

$=0.4708 \mathrm{~m}^{2}$

Hence, $0.4708$ square metres of the metal sheet would be needed to make the cylindrical vessel.

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Updated on: 10-Oct-2022

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