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 $=28 \times 11 \times h=770 \mathrm{~m}^{3}$
$\therefore h=\frac{770}{28 \times 11}=\frac{70}{28}=2.5 \mathrm{~m}$