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

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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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