# A well of 11.2m diameter is dug 8m deep.the earth taken out has been spread all around it to a width of 7m to form a circular embankment.find the height of embankment

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by jsai

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by jsai

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So we know well is cylinder

radius = 11.2 /2 = 5.6 m

height = 8 m

so volume of earth dig

πr²h

= 22/7 × 5.4² × 8

= 787.76 m³

so spreading will create a hollow cylinder

let the height be h

so

formula for volume of hollow sphere is

πh(r₂²-r₁²)

787.76 = πh(12.4²-5.6²)

h=787.76/π(12.4²-5.6²)

h = 1.97 m

radius = 11.2 /2 = 5.6 m

height = 8 m

so volume of earth dig

πr²h

= 22/7 × 5.4² × 8

= 787.76 m³

so spreading will create a hollow cylinder

let the height be h

so

formula for volume of hollow sphere is

πh(r₂²-r₁²)

787.76 = πh(12.4²-5.6²)

h=787.76/π(12.4²-5.6²)

h = 1.97 m

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Diameter of well = 11.2m

radius(r) = 5.6m

depth (h) = 8m

The earth taken out = The volume of the well = V

V = πr²h = π×5.6²×8 m³

As the volume of earth taken has been used to make the embankment, the volume of embankment is the same as volume of well.

A circular embankment is a hollow cylinder with some width

In this case width(w) = 7m.

The inner radius of embankment(r1) = 5.6m (same as the well)

outer radius of embankment(r2) = (r1+w) = (5.6+7)m = 12.6m

Let the height = h1 m

Volume of embankment = volume of well

⇒π×h1×[(r2)² - (r1)²] = πr²h

⇒ π×h1×[(r2)² - (r1)²] = π×5.6²×8

⇒ h1×[12.6² - 5.6²] = 5.6²×8

⇒ h1 = (5.6²×8) / (12.6²-5.6²)

⇒ h1 = 1.97m

Height of embankment is**1.97m**

radius(r) = 5.6m

depth (h) = 8m

The earth taken out = The volume of the well = V

V = πr²h = π×5.6²×8 m³

As the volume of earth taken has been used to make the embankment, the volume of embankment is the same as volume of well.

A circular embankment is a hollow cylinder with some width

In this case width(w) = 7m.

The inner radius of embankment(r1) = 5.6m (same as the well)

outer radius of embankment(r2) = (r1+w) = (5.6+7)m = 12.6m

Let the height = h1 m

Volume of embankment = volume of well

⇒π×h1×[(r2)² - (r1)²] = πr²h

⇒ π×h1×[(r2)² - (r1)²] = π×5.6²×8

⇒ h1×[12.6² - 5.6²] = 5.6²×8

⇒ h1 = (5.6²×8) / (12.6²-5.6²)

⇒ h1 = 1.97m

Height of embankment is