Question

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

Answer 1

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$\huge\mathcal\purple{Solution:-}$

Answer:

Height of the embankment = 4.66 m.

Step-by-step explanation:

We have,

Volume of the earth dug out= πr²h m³

= 22/7 × 5 × 5 × 14m³ = 1100 m³

Area of the embankment (shaded region)

= π (R² - r²)

=> Area of the embankment (shaded region)

= π (10² - 5²) m²

= 22/7 × 75 m²

Now,

Let h be the height of the embankment. Then,

Volume of the hollow cylinder = Volume of the earth dugout.

=> π (R² - r²) h = 1100

=> 22/7 × (100 - 25) × h= 1100

=> h= 1100×7/ 22 ×75 m

=> h= 14/3 m

=> h= 4.66 m.

Therefore,

→ Height of the embankment

= Volume of the earth dugout/Area of the embankment

→ Height of the embankment

$\frac{1100}{ \frac{22}{7} \times 75 }$

= 7 × 1100/ 22 × 75

= 4.66 m. [The required solution..]

#Aliter :- The earth dugout when spread around the well forms va hollow cylinder of external and internal radii R = 10 m and r= 5 m respectively.

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Answer 2

Answer:

Let the height of embankment be x.

Volume of earth taken out =volume of earth used to form embankment

14*10=5*x

140=5*x

140/5=x

28 = x

Height of embankment = 28 m

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