Question

A well, whose diameter is 3 m, has been dug 21 m deep and the earth dug out is used to form an embankment 4 m wide around it. Find the height of the embankment.

Answer 1

31.875 m

Explanation:

We can begin solving the problem by using the formula for the volume of a cylinder and the volume of a cone.

The volume of the well is given by the formula for the volume of a cylinder:

V = πr^2h

where r is the radius of the well (half the diameter, which is 3/2 = 1.5 m) and h is the depth of the well (21 m).

V = π(1.5)^2(21) = 42.5π m^3

The embankment is formed by the earth that was dug out of the well, and it has the shape of a cone. The volume of the cone is given by the formula:

V = 1/3 πr^2h

where r is the radius of the base of the cone (4 m) and h is the height of the embankment.

V = 1/3π(4)^2h = 4/3πh m^3

Now we know that the volume of the embankment is equal to the volume of the well:

V = 42.5π m^3 = 4/3πh m^3

Then we can solve for h by dividing both sides by 4/3π:

h = 42.5π m^3 * 3/4π = 31.875 m

So the height of the embankment is 31.875 m.