Question

a well is to be dug with 4m inside diameter and 10 m in depth find the quantity of earth to be excavated the earth taken out is spread all around the to a width of 4m to form an embankment .find the height of the embankment

Answer 1

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Answer 2

Given,

Dimensions of a well to be dug;

Inner diameter = 4 meters

depth = 10 meters

Width of the embankment to be formed around the well = 4 meters

To find,

The height of the embankment.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the height of the embankment is equal to h meters.

As per mensuration;

The volume of a cylinder = π x (radius)^2 x height

The volume of a hollow cylinder = π x {(outer radius)^2 - (inner radius)^2} x height

Now,

according to the question;

The volume of earth dugout

= volume of the well (cylinder-shaped) = volume of the embankment (hollow cylinder-shaped)

=> π x (radius of well)^2 x (height of the well) = π x {(outer radius)^2 - (inner radius)^2} x (height of the embankment)

=> (diameter of the well/2)^2 x (height of the well) = {(radius of the well + width of the embankment)^2 - (radius of the well)^2} x (height of the embankment)

=> (2 m)^2 x (10 m) = {(2 m + 4 m)^2 - (2 m)^2} x (h)

=> 4 m^2 x (10 m) = {(6 m)^2 - (2 m)^2} x (h)

=> 40 m^3 = {36 m^2 - 4 m^2} x (h)

=> h = 40/32 meters

=> h = 1.25 meters

Hence, the height of the embankment is equal to 1.25 meters.