A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is $70\ cm$ and its height is $1.4\ m$, calculate the cost of tin-coating at the rate of $Rs.\ 3.50$ per $1000\ cm^2$.

Given:

A cylindrical vessel, without lid, has to be tin-coated on its both sides.

The radius of the base is $70\ cm$ and its height is $1.4\ m$.

To do:

We have to find the cost of tin-coating at the rate of $Rs.\ 3.50$ per $1000\ cm^2$.

Solution:

Radius of the base of the cylindrical vessel $(r) = 70\ cm$

Height of the cylinder $(h) = 1.4\ m$

$= 1.4\times100\ cm$

$=140\ cm$

Total surface area (excluding upper lid) on both sides $= 2 \pi rh \times 2 + \pi r^2 \times 2$

$=4 \pi r h+2 \pi r^{2}$

$=\pi r(4 h+2 r)$

$=\frac{22}{7} \times 70[4 \times 140+70 \times 2]$

$=220[560+140]$

$=220 \times 700$

$=154000 \mathrm{~cm}^{2}$

Rate of tin coating $= Rs.\ 3.50$ per $1000 \mathrm{~cm}^{2}$

Total cost of coating $=\frac{154000 \times 3.50}{1000}$

$=Rs.\ 154 \times 3.50$

$=Rs.\ 539$

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Updated on: 10-Oct-2022

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