How many cubic metres of earth must be dug out to sink a well which is 20 m deep and has a diameter of 7 metres?

Question:

How many cubic metres of earth must be dug out to sink a well which is 20 m deep and has a diameter of 7 metres? If the earth so dug out is spread over a rectangular plot 28 m by 11 m, what is the height of the platform so formed?

Solution:

Diameter $=7 \mathrm{~m}$

Radius $=3.5 \mathrm{~m}$

Depth $=20 \mathrm{~m}$

Volume of the earth dug out $=\pi r^{2} \mathrm{~h}=\frac{22}{7} \times 3.5 \times 3.5 \times 20=770 \mathrm{~m}^{3}$

Volume of the earth piled upon the given plot $=28 \times 11 \times h=770 \mathrm{~m}^{3}$

$\therefore h=\frac{770}{28 \times 11}=\frac{70}{28}=2.5 \mathrm{~m}$

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