Question

a well with 20m inside diameter is dug 7m deep. earth taken out of it is spread all around to a width of 3m to form an embankment. find the height of the embankment.

Answer 1

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Answer 2

Answer:

The height of the embankment is 10.14 m.

Step-by-step explanation:

Given : A well with 20m inside diameter is dug 7m deep. Earth taken out of it is spread all around to a width of 3m to form an embankment.

To find : The height of the embankment?

Solution :

A well with 20m inside diameter is dug 7m deep

Radius of the well = 10 m

Volume of the well is

$V=\pi r^{2} h$

$V=\frac{22}{7} 10^{2} \times 7$

$V=22\times 100$

$V=2200m^3$

Now, it is spread to form embankment, which is in the form of hollow cylinder,

Inner radius, r= 10 m

Outer radius = 10 +3 = 13 m

height= h

Volume of the earth spread=volume of the well

$\pi (R^2-r^2)h=2200$

$\frac{22}{7}\times (13^2-10^2)h=2200$

$(169-100)h=\frac{2200\times 7}{22}$

$69h=700$

$h=10.14m$

Therefore, The height of the embankment is 10.14 m.