Find the cost of sinking a tubewell $280\ m$ deep, having diameter $3\ m$ at the rate of $Rs.\ 3.60$ per cubic metre. Find also the cost of cementing its inner curved surface at $Rs.\ 2.50$ per square metre.

 Given:

A tubewell is $280\ m$ deep and a diameter $3\ m$.

The rate of sinking the tubewell $=Rs.\ 3.60$ per cubic metre. 

To do:

We have to find the cost of sinking a tubewell and the cost of cementing its inner curved surface at $Rs.\ 2.50$ per square metre.

Solution:

Depth of the well $(h) = 280\ m$

Diameter of the well $= 3\ m$
Therefore,

Radius $(r)=\frac{3}{2} \mathrm{~m}$

Volume of the earth dugout $=\pi r^{2} h$

$=\frac{22}{7} \times \frac{3}{2} \times \frac{3}{2} \times 280$

$=1980 \mathrm{~m}^{3}$

Rate of sinking the tubewell $= Rs.\ 3.60$ per $\mathrm{m}^{3}$

Total cost of sinking the tubewell $=Rs.\ 3.60 \times 1980$

$= Rs.\ 7128$

Area of the inner curved surface $=2 \pi r h$

$=2 \times \frac{22}{7} \times \frac{3}{2} \times 280$

$=2640 \mathrm{~m}^{2}$

Rate of cementing $=Rs.\ 2.50$ per $\mathrm{m}^{2}$

This implies,

Total cost of cementing $= Rs.\ 2.50 \times 2640$

$=Rs.\ 6600$

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Updated on: 10-Oct-2022

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