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Question

 A well of inner diameter 14 M is  dug to a depth of 15 M Earth taken out it has been evenly spread out around it to our weight of 7 meter to form an embankment find the height of embankment so formed


Solution

Here, a well is dug and Earth taken out of it is used to form an embankment.

Given:

Inner Diameter of the well= 14 m

Inner Radius of the well (r) = 14/2 m = 7 m

Height of the well(h) = 15 m

Volume of the earth taken out of the well = πr²h 

= 22/ 7 ×(7)²×15 

= 22× 7×15= 2310 m³

Width= 7m 

Outer radius of the embankment R =inner radius + width

Outer radius (R)= 7 + 7 = 14m

The embankment is in the form of cylindrical shell, so area of embankment


Area of embankment = outer area - inner area

= πR² - πr² = π(R²-r²)

= (22/7) ( 14² - 7²)

= 22/7(196-49)

= 22/7 × 147

= 22 × 21

= 462 m²


Volume of embankment= volume of earth taken out on digging the well

Area of embankment × height of embankment= volume of earth dug out

Height of embankment= volume of earth dug out/area of the embankment

Height of the embankment = 2310 / 462

Height of embankment= 5 m

Hence, the height of the embankment so formed is 5 m ====================================================

 

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