How many cubic metres of earth must be dugout to sink a well $21\ m$ deep and $6\ m$ diameter? Find the cost of plastering the inner surface of the well at Rs. $9.50$ per $m^2$.

 Given:

A well is $21\ m$ deep and $6\ m$ in diameter.

To do:

We have to find the volume of the earth that must be dugout and the cost of plastering the inner surface of the well at Rs. $9.50$ per $m^2$.

Solution:

Diameter of the well $= 6\ m$

This implies,

Radius $(r) =\frac{6}{2}$

$= 3\ m$

Depth of the well $(h) = 21\ m$

Therefore,

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

$=\frac{22}{7} \times 3 \times 3 \times 21$

$=594 \mathrm{~m}^{3}$

Curved surface area $=2 \pi r h$

$=2 \times \frac{22}{7} \times 3 \times 21$

$=396 \mathrm{~m}^{2}$

Rate of plastering the surface $= Rs.\ 9.50$ per $\mathrm{m}^{2}$

Total cost of plastering $=Rs.\ 9.50 \times 396$

$= Rs.\ 3762$

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Updated on: 10-Oct-2022

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