How many cubic metres of earth must be dug out to sink a well of $ 22.5 \mathrm{~m} $ deep and diameter $ 7 \mathrm{~m} $? Also, find the cost of plastering the inner curved surface at Rs. 3 per square metre.

Given:

Depth of the well$h=22.5\ m$

Diameter of the well$=7\ m$

Cost of plastering the inner curved surface$=Rs.\ 3$ per square metre.
To do:

We have to find the total cost of plastering the inner curved surface.

Solution:

Radius of the well$r=\frac{7}{2}\ m$.

Volume of the earth that must be dug out$=$Volume of the well

$=\pi r^2h$

$=\frac{22}{7}\times(\frac{7}{2})^2\times22.5\ m^3$

$=\frac{11\times7}{2}\times22.5\ m^3$

$=866.25\ m^3$

Curved surface area of the well$=2\pi rh$

$=2\times\frac{22}{7}\times\frac{7}{2}\times22.5\ m^2$

$=22\times22.5\ m^2$

$=495\ m^2$

Cost of plastering $495\ m^2$ of curved surface area of the well$=Rs.\ 495\times3$

$=Rs.\ 1485$.

Therefore,

$866.25$ cubic metres of earth must be dug out to sink a well of \( 22.5 \mathrm{~m} \) deep and diameter \( 7 \mathrm{~m} \) and the cost of plastering the inner curved surface at Rs. 3 per square metre is Rs. 1485.

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Updated on: 10-Oct-2022

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