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  • A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.   <div style="float:lef

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

 

 

 

 
 
 
 
 

Answers (1)

Height of the well =14 \; m

Diameter of the well =3 \; m

\text{So, radius of the well}= \frac{3}{2} \; m

Volume of the earth taken out of the well

=\pi r^2h

=\frac{22}{7}\times \left ( \frac{3}{2} \right )^2\times 14

=\frac{22}{7}\times \frac{9}{4}\times 14

=99 \; m^3

Other radius of the embankment 

R=\left ( \frac{3}{2}+4 \right )\; m =\frac{11}{2}\; m

\text{Area of embankment}=\text{Outer area}-\text{Inner area}

                                               =\pi R^2-\pi r^2

                                        =\frac{22}{7}\left [ \left ( \frac{11}{2} \right )^2 - \left ( \frac{3}{2} \right )^2 \right ]

                                        =\frac{22}{7}\left [ \frac{121}{4} - \frac{9}{4} \right ]

                                        =\frac{22}{7} \times \frac{112}{4}

                                        =88\; m^2

\text{Height of embankment}=\frac{\text{Volume}}{\text{Area}}

                                                   = \frac{99}{88}

Height of embankment is 1.125 meter

Posted by

Ravindra Pindel

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