A well is daimeter of 14m and its height is 50m is dugout and the soil os evenlyspread around it to form an embankment of width 2m. Find its height
Answers
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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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Answer:
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