Question

) A well with inner diameter 8m is dug 14 m deep. Earth taken Out of it has been spread even all around it to a width of 3 m to Form an embankment. Find the height of the embankment ?
{ Ans : 6.78 m }

Answer 1

Solution :

Inner diameter of the well : 8 m .

So , radius of the well ( inner radii ) is 4 m .

The well is dug 14 m deep .

So , the volume of earth dug out becomes ;

=> Volume of the cylinder formed by the well ( Assuming that the well is perfect geometrically )

=> ( π r² ) × h

=> ( 16 π ) × 14

=> 16 × 22/7 × 14

=> 16 × 22 × 2

=> 44 × 16

=> 704 m³ .

This is spread around it to a width of 3m .

So , new diameter becomes 8 + 3 = 11 m

New Radii = 5.5 m ( Outer radii )

Cross sectional Area of embankment

=> π ( 5.5 )² - π ( 4 )²

=> π ( 9.5 )( 1.5 )

=> 14.25 π

Height Of Embankment

=> ( 704 / 14.25π ) m

=> 6.78 m approx .

This is the required answer .

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