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Mathematics

How many cubic metres of soil must be take out to make a well 20 metres deep and 2 metres in diameter?

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Answer

A well needs to be formed which is 20 meters deep and has a diameter of 2 meters.

Height of well (h) = 20 m

Radius (r) = Diameter2=22\dfrac{\text{Diameter}}{2} = \dfrac{2}{2} = 1 m

Volume of soil to be dug out = Volume of well to be formed.

Volume of well = πr2h.

Substituting values we get,

Volume of well =227×(1)2×20=227×1×20=4407=6267.\text{Volume of well }= \dfrac{22}{7} \times (1)^2 \times 20 \\[1em] = \dfrac{22}{7} \times 1 \times 20 \\[1em] = \dfrac{440}{7} \\[1em] = 62\dfrac{6}{7}.

Hence, 626762\dfrac{6}{7} m3 of soil must be dug out for the formation of well.

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