A well of inner dimensions 14m is dug to a depth of 12m. Earth taken out of it has been evenly spread all around it to a width of 7m to form an embankment. Find the height of the embankment so formed.
Answers
Answer:
the height of the embankment so formed is 5 m
Step-by-step explanation:
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 ==================================================================
Hope this will help you.....