Question

A well with 10m inside diameter is dug 14m deep. Earth is taken out of it is spread all around to the width of 5m to form a embankment. Find the height of the embankment?..mi ali​

Answer 1

Solution :

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{5 \: m}}\put(9,17.5){\sf{14 \: m }}\end{picture}$

r = 5m

h = 14 m

Volume of earth extracted >> πr²h >> (22/7) × 25 × 14

>> 44 × 25

>> 4 × 11 × 25

>> 100 × 11 = 1100 m³

Now, the earth is spread all around to the with of 5m to form an embankment.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(1.2,0)(1.121,1.121)(0,1.2)\qbezier(1.2,0)(1.121,-1.121)(0,-1.2)\qbezier(0,-1.2)(-1.121,-1.121)(-1.2,0)\qbezier(-1.2,0)(-1.121,1.121)(0,1.2)\put(-0,0){\vector(-1,0){2.3}}\put(0,0){\vector(0,1){1.2}}\put(-1.9,0.2){ \bf R \: = 10 \: m }\put(0.2,0.3){ \bf r \: = 5 \: m }\end{picture}$

Base area >> πR² - πr² >> π( 100 - 25) >> 75π

Suppose the height of the embankment is h m

75πh = 1100

Dividing by 25

3πh = 44

3×(22/7) × h = 44

(3/7) h = 2

>> h = 14/3 m ≈4.7 m.

This is the required answer.

____________________________________