A well with 10m inside diameter is dug 14m deep. Earth taken out of it is spread all around to a width of 5m to form an embankment; the height of the embankment is ____________

A. 2.46 mB. 3.56 mC. 4.66 mD. 5.75 m

To solve this problem, we need to find the height of the embankment.

Step 1: Volume of Earth taken out of the well
The well is in the shape of a cylinder. The formula to calculate the volume of a cylinder is:

Volume = π × r² × h

where:

r is the radius of the cylinder (half of the diameter),
h is the height (depth) of the well.
The diameter of the well is 10m, so the radius (r) = 10 / 2 = 5m.
The depth (h) of the well is 14m.

Volume of the well = π × (5)² × 14
Volume = π × 25 × 14
Volume = 350π m³

So, the total volume of the earth taken out from the well is 350π m³.

Step 2: Volume of the embankment
The embankment is formed by spreading the earth around the well. The embankment has the shape of a ring (annular region), with the outer radius of the embankment being the radius of the well plus the width of the embankment.

The radius of the well = 5m
The width of the embankment = 5m
Therefore, the outer radius of the embankment = 5 + 5 = 10m
The volume of the embankment is the volume of the outer cylinder minus the volume of the inner cylinder (the well).

The formula for the volume of a cylindrical ring is:

Volume = π × (R² - r²) × h

where:

R is the outer radius (10m),
r is the inner radius (5m),
h is the height of the embankment, which we need to find.
The volume of the embankment is equal to the volume of earth taken out from the well, i.e., 350π m³.

So, we set up the equation:

350π = π × (10² - 5²) × h

Simplifying the equation:

350π = π × (100 - 25) × h
350π = π × 75 × h

Now, divide both sides by π:

350 = 75 × h

Solving for h:

h = 350 / 75
h = 4.66 meters

Final Answer:
The height of the embankment is 4.66 meters.

So, the correct answer is:

C. 4.66 m