question_answer

A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.

Answer:

Given, diameter and height of cylindrical well are 4 m and 21 m respectively.

Now, the earth has been taken out to spread evenly all around.

Then, volume of earth dug out \[=\frac{22}{7}\times \frac{3}{4}\times \frac{1}{3}\times 21\]\[=264\,{{m}^{3}}\]

And the volume of embankment of width 3 m which forms a shape of circular ring \[=\pi ({{(5)}^{2}}-{{(2)}^{2}})\times h\]

\[=\frac{22}{7}(25-4)\times h=66\,h\,{{m}^{3}}\]

[\[\because \] Outer radius \[=2+3=5\,cm\]]

\[\because \] Volume of earth dug out = Volume of embankment

\[\therefore 264=66h\]

\[\Rightarrow h=\frac{264}{66}=4\,m\]

Hence, the height of the embankment is 4 m.