Question

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$<b>A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of the embankment so formed .</b>$​

Answer 1

${\huge {\mathfrak {Answer :-}}}$

Inner diameter = 14.

Inner radius = 14/2 = 7 m.

So, Volume of the well

= 22/7 * 7 * 7 * 12 m^3

= 154 * 12 m^3

= 1848 m^3

Thus, Volume of earth taken out is 1848 m^3.

Thus, Volume of the embankment = 1848 m^3.

Now, Let the height be h.

So, l * b * h = 1848

Or, l * h = 1848/7 = 264

Or, h = 264/l

Here, ' l ' refers to length of the embankment that is not mentioned in the question.

So, I can't do anything

$<i>$ That's it..

Answer 2

➡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.....