Question

A well with 40 m internal diameter is dug 14 m deep. The soil taken out is spread all around to a width of
20 m to form a circular embankment, find the height of the embankment.
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Answer 1

Given:-

• Diameter of well = 40m

• Height of well = 14m

• width of embankment = 20m

To Find:-

• The height of the embarkment

Formulae used:-

• Volume of Hollow cylinder = πR²h - πr²h

Now,

→ Radius of well = 40/2 = 20m

→ Height of well = 14m

→ Volume of soil taken out = πr²h

→ 22/7 × 20 × 20 × 14

→ 22 × 400 × 2

→ 17600m³ is taken out to made a embankment of width 20m

→ R = 20 + 20 = 40

→ r = 20m

Therefore,

→ πR²h - πr²h = 17600

→ π( R² - r² )h = 17600

→ 22(R² - r²)h = 17600 × 7

→ (R² - r²)h = 5600

→ ((40)² - (20)²)h = 5600

→ (1600 - 400)h = 5600

→ 1200h = 5600

→ h = 5600/1200

→ h = 56/12

→ h = 4.66m

Hence, The Height of embankment is 4.66m

** See the attachment for better understanding*

Answer 2

Answer:

Given :-

• Internal Diameter = 40 m
• Height of wall = 14 m
• Width of embankment = 20 m

To Find :-

Height

Solution :-

Radius = D/2

Radius = 40/2 = 20 m

Now,

Finding soil taken

Volume of soil taken out =Volume of cylinder

= πr²h

22/7 × 20 × 20 × 14

22 × 400 × 2

44 × 400

17600 m³

Now,

R = 20 + 20 = 40 m

r = 20 m

πR²h - πr²h = 17600

π( R² - r² )h = 17600

22(R² - r²)h = 17600 × 7

(R² - r²)h = 5600

{(40)² - (20)²} = 5600

(1600 - 400)h = 5600

(1200h)= 5600

h = 5600/1200

h = 4.66m

Hence :-

Height of embankment is 4.66 m