Question

A well of diameter 2m is dug 14m deep. The earth taken out of it is spread evenly all around it to a width of 5m to form an embankment. Find the height of the embankment.

Please I need the answer urgently. I cannot give a rest to my curiosity

Answer 1

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Answer 2

Answer: The height of the embankment is 40 cm.

Step-by-step explanation:

Since we have given that

Diameter of a well = 2 m

Radius of a well = 1 m

Height of a well = 14 m

So, Volume of a well is given by

$\pi r^2h\\\\=\frac{22}{7}\times 1\times 1\times 14\\\\=22\times 2\\\\=44\ m^2$

Now, the earth taken out of it is spread evenly all around it to a width of 5 m to form an embankment.

so, Outer Radius of embankment = 1+5 = 6 m

So, Volume of embankment is given by

$\pi (R^2-r^2)\times h\\\\=\frac{22}{7}\times (6^2-1^2)\times h\\\\=\frac{22}{7}\times 35\times h$

Since the earth of a well is used to form an embankment so, their volume must be equal .

Volume of embankment = Volume of well

$\frac{22}{7}\times 35\times h=44\\\\h=\frac{44\times 7}{22\times 35}\\\\h=\frac{2}{5}\ m\\\\h=\frac{2}{5}\times 100\ cm\\\\h=40\ cm$

Hence, the height of the embankment is 40 cm.